diff --git a/doc/opengl-mapping.dox b/doc/opengl-mapping.dox
index b2bbb7566..68177a9c4 100644
--- a/doc/opengl-mapping.dox
+++ b/doc/opengl-mapping.dox
@@ -175,7 +175,7 @@ OpenGL function                         | Matching API
 @fn_gl2{GetBufferPointer,GetBufferPointerv}, \n `glGetNamedBufferPointer()`, \n @fn_gl_extension{GetNamedBufferPointer,EXT,direct_state_access} | not queryable, @ref Buffer::map() setter only
 @fn_gl{GetBufferSubData}, \n `glGetNamedBufferSubData()`, \n @fn_gl_extension{GetNamedBufferSubData,EXT,direct_state_access} | @ref Buffer::data(), \n @ref Buffer::subData()
 @fn_gl{GetCompressedTexImage}, \n `glGetnCompressedTexImage()`, \n @fn_gl_extension{GetnCompressedTexImage,ARB,robustness}, \n `glGetCompressedTextureImage()`,  \n @fn_gl_extension{GetCompressedTextureImage,EXT,direct_state_access} | @ref Texture::compressedImage(), \n @ref TextureArray::compressedImage(), \n @ref CubeMapTexture::compressedImage(), \n @ref CubeMapTextureArray::compressedImage(), \n @ref RectangleTexture::compressedImage()
-@fn_gl{GetCompressedTextureSubImage}    | |
+@fn_gl{GetCompressedTextureSubImage}    | @ref Texture::compressedSubImage(), \n @ref TextureArray::compressedSubImage(), \n @ref CubeMapTexture::compressedImage(), \n @ref CubeMapTexture::compressedSubImage(), \n @ref CubeMapTextureArray::compressedSubImage(), \n @ref RectangleTexture::compressedSubImage()
 @fn_gl{GetDebugMessageLog}              | |
 @fn_gl{GetError}                        | @ref Renderer::error()
 @fn_gl{GetFragDataIndex}, @fn_gl{GetFragDataLocation} | not queryable, @ref AbstractShaderProgram::bindFragmentDataLocation() and \n @ref AbstractShaderProgram::bindFragmentDataLocationIndexed() setters only
diff --git a/doc/opengl-support.dox b/doc/opengl-support.dox
index 2a39b4ed4..f8ac8924b 100644
--- a/doc/opengl-support.dox
+++ b/doc/opengl-support.dox
@@ -222,7 +222,7 @@ GLSL 4.50                                   | done
 @extension{ARB,cull_distance}               | |
 @extension{ARB,derivative_control}          | done (shading language only)
 @extension{ARB,direct_state_access}         | done for implemented functionality (except VAOs)
-@extension{ARB,get_texture_sub_image}       | missing compressed texture queries
+@extension{ARB,get_texture_sub_image}       | done
 @extension{ARB,shader_texture_image_samples} | done (shading language only)
 @extension{ARB,texture_barrier}             | |
 @extension{KHR,context_flush_control}       | |
diff --git a/src/Magnum/AbstractTexture.cpp b/src/Magnum/AbstractTexture.cpp
index d4fc418a5..94012890d 100644
--- a/src/Magnum/AbstractTexture.cpp
+++ b/src/Magnum/AbstractTexture.cpp
@@ -1629,6 +1629,64 @@ template<UnsignedInt dimensions> void AbstractTexture::subImage(const GLint leve
 template void MAGNUM_EXPORT AbstractTexture::subImage<1>(GLint, const Range1Di&, BufferImage<1>&, BufferUsage);
 template void MAGNUM_EXPORT AbstractTexture::subImage<2>(GLint, const Range2Di&, BufferImage<2>&, BufferUsage);
 template void MAGNUM_EXPORT AbstractTexture::subImage<3>(GLint, const Range3Di&, BufferImage<3>&, BufferUsage);
+
+template<UnsignedInt dimensions> std::size_t AbstractTexture::compressedSubImageSize(TextureFormat format, const Math::Vector<dimensions, Int>& size) {
+    /* Amount of blocks in given range (rounded up) multiplied by block
+       data size. The user is responsible for proper block-aligned size. */
+    const Math::Vector<dimensions, Int> blockSize = DataHelper<dimensions>::compressedBlockSize(_target, format);
+    return ((size + blockSize - Math::Vector<dimensions, Int>{1})/blockSize).product()*
+        compressedBlockDataSize(_target, format);
+}
+
+template<UnsignedInt dimensions> void AbstractTexture::compressedSubImage(const GLint level, const RangeTypeFor<dimensions, Int>& range, CompressedImage<dimensions>& image) {
+    createIfNotAlready();
+
+    const Math::Vector<dimensions, Int> size = range.size();
+    const Vector3i paddedOffset = Vector3i::pad(range.min());
+    const Vector3i paddedSize = Vector3i::pad(size, 1);
+    GLint format;
+    (this->*Context::current()->state().texture->getLevelParameterivImplementation)(level, GL_TEXTURE_INTERNAL_FORMAT, &format);
+    const std::size_t dataSize = Implementation::compressedImageDataSizeFor(image, size, compressedSubImageSize<dimensions>(TextureFormat(format), size));
+
+    /* Reallocate only if needed */
+    Containers::Array<char> data{image.release()};
+    if(data.size() < dataSize)
+        data = Containers::Array<char>{dataSize};
+
+    Buffer::unbindInternal(Buffer::TargetHint::PixelPack);
+    image.storage().applyPack();
+    glGetCompressedTextureSubImage(_id, level, paddedOffset.x(), paddedOffset.y(), paddedOffset.z(), paddedSize.x(), paddedSize.y(), paddedSize.z(), data.size(), data);
+    image.setData(CompressedPixelFormat(format), size, std::move(data));
+}
+
+template void MAGNUM_EXPORT AbstractTexture::compressedSubImage<1>(GLint, const Range1Di&, CompressedImage<1>&);
+template void MAGNUM_EXPORT AbstractTexture::compressedSubImage<2>(GLint, const Range2Di&, CompressedImage<2>&);
+template void MAGNUM_EXPORT AbstractTexture::compressedSubImage<3>(GLint, const Range3Di&, CompressedImage<3>&);
+
+template<UnsignedInt dimensions> void AbstractTexture::compressedSubImage(const GLint level, const RangeTypeFor<dimensions, Int>& range, CompressedBufferImage<dimensions>& image, const BufferUsage usage) {
+    createIfNotAlready();
+
+    const Math::Vector<dimensions, Int> size = range.size();
+    const Vector3i paddedOffset = Vector3i::pad(range.min());
+    const Vector3i paddedSize = Vector3i::pad(size, 1);
+    GLint format;
+    (this->*Context::current()->state().texture->getLevelParameterivImplementation)(level, GL_TEXTURE_INTERNAL_FORMAT, &format);
+    const std::size_t dataSize = Implementation::compressedImageDataSizeFor(image, size, compressedSubImageSize<dimensions>(TextureFormat(format), size));
+
+    /* Reallocate only if needed */
+    if(image.dataSize() < dataSize)
+        image.setData(image.storage(), CompressedPixelFormat(format), size, {nullptr, dataSize}, usage);
+    else
+        image.setData(image.storage(), CompressedPixelFormat(format), size, nullptr, usage);
+
+    image.buffer().bindInternal(Buffer::TargetHint::PixelPack);
+    image.storage().applyPack();
+    glGetCompressedTextureSubImage(_id, level, paddedOffset.x(), paddedOffset.y(), paddedOffset.z(), paddedSize.x(), paddedSize.y(), paddedSize.z(), dataSize, nullptr);
+}
+
+template void MAGNUM_EXPORT AbstractTexture::compressedSubImage<1>(GLint, const Range1Di&, CompressedBufferImage<1>&, BufferUsage);
+template void MAGNUM_EXPORT AbstractTexture::compressedSubImage<2>(GLint, const Range2Di&, CompressedBufferImage<2>&, BufferUsage);
+template void MAGNUM_EXPORT AbstractTexture::compressedSubImage<3>(GLint, const Range3Di&, CompressedBufferImage<3>&, BufferUsage);
 #endif
 #endif
 
diff --git a/src/Magnum/AbstractTexture.h b/src/Magnum/AbstractTexture.h
index 2921da856..2b1657aa9 100644
--- a/src/Magnum/AbstractTexture.h
+++ b/src/Magnum/AbstractTexture.h
@@ -409,6 +409,8 @@ class MAGNUM_EXPORT AbstractTexture: public AbstractObject {
         template<UnsignedInt dimensions> void compressedImage(GLint level, CompressedBufferImage<dimensions>& image, BufferUsage usage);
         template<UnsignedInt dimensions> void subImage(GLint level, const RangeTypeFor<dimensions, Int>& range, Image<dimensions>& image);
         template<UnsignedInt dimensions> void subImage(GLint level, const RangeTypeFor<dimensions, Int>& range, BufferImage<dimensions>& image, BufferUsage usage);
+        template<UnsignedInt dimensions> void compressedSubImage(GLint level, const RangeTypeFor<dimensions, Int>& range, CompressedImage<dimensions>& image);
+        template<UnsignedInt dimensions> void compressedSubImage(GLint level, const RangeTypeFor<dimensions, Int>& range, CompressedBufferImage<dimensions>& image, BufferUsage usage);
         #endif
 
         GLenum _target;
@@ -431,6 +433,10 @@ class MAGNUM_EXPORT AbstractTexture: public AbstractObject {
         void MAGNUM_LOCAL createImplementationDSA();
         #endif
 
+        #ifndef MAGNUM_TARGET_GLES
+        template<UnsignedInt dimensions> std::size_t MAGNUM_LOCAL compressedSubImageSize(TextureFormat format, const Math::Vector<dimensions, Int>& size);
+        #endif
+
         void MAGNUM_LOCAL bindImplementationDefault(GLint textureUnit);
         #ifndef MAGNUM_TARGET_GLES
         void MAGNUM_LOCAL bindImplementationMulti(GLint textureUnit);
diff --git a/src/Magnum/CubeMapTexture.cpp b/src/Magnum/CubeMapTexture.cpp
index f29e4ea51..49d2ef01a 100644
--- a/src/Magnum/CubeMapTexture.cpp
+++ b/src/Magnum/CubeMapTexture.cpp
@@ -257,6 +257,16 @@ BufferImage3D CubeMapTexture::subImage(const Int level, const Range3Di& range, B
     return std::move(image);
 }
 
+CompressedImage3D CubeMapTexture::compressedSubImage(const Int level, const Range3Di& range, CompressedImage3D&& image) {
+    compressedSubImage(level, range, image);
+    return std::move(image);
+}
+
+CompressedBufferImage3D CubeMapTexture::compressedSubImage(const Int level, const Range3Di& range, CompressedBufferImage3D&& image, const BufferUsage usage) {
+    compressedSubImage(level, range, image, usage);
+    return std::move(image);
+}
+
 CubeMapTexture& CubeMapTexture::setSubImage(const Int level, const Vector3i& offset, const ImageView3D& image) {
     createIfNotAlready();
 
diff --git a/src/Magnum/CubeMapTexture.h b/src/Magnum/CubeMapTexture.h
index dda1c8861..2ee70927a 100644
--- a/src/Magnum/CubeMapTexture.h
+++ b/src/Magnum/CubeMapTexture.h
@@ -721,6 +721,50 @@ class MAGNUM_EXPORT CubeMapTexture: public AbstractTexture {
          * @endcode
          */
         BufferImage3D subImage(Int level, const Range3Di& range, BufferImage3D&& image, BufferUsage usage);
+
+        /**
+         * @copybrief Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedImage&)
+         *
+         * See @ref Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedImage&)
+         * for more information.
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         * @requires_gl Texture image queries are not available in OpenGL ES or
+         *      WebGL. See @ref Framebuffer::read() for possible workaround.
+         */
+        void compressedSubImage(Int level, const Range3Di& range, CompressedImage3D& image) {
+            AbstractTexture::compressedSubImage<3>(level, range, image);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedImage3D image = texture.compressedSubImage(0, range, {});
+         * @endcode
+         */
+        CompressedImage3D compressedSubImage(Int level, const Range3Di& range, CompressedImage3D&& image);
+
+        /**
+         * @copybrief Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedBufferImage&, BufferUsage)
+         *
+         * See @ref Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedBufferImage&, BufferUsage)
+         * for more information.
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         * @requires_gl Texture image queries are not available in OpenGL ES or
+         *      WebGL. See @ref Framebuffer::read() for possible workaround.
+         */
+        void compressedSubImage(Int level, const Range3Di& range, CompressedBufferImage3D& image, BufferUsage usage) {
+            AbstractTexture::compressedSubImage<3>(level, range, image, usage);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedBufferImage3D image = texture.compressedSubImage(0, range, {}, BufferUsage::StaticRead);
+         * @endcode
+         */
+        CompressedBufferImage3D compressedSubImage(Int level, const Range3Di& range, CompressedBufferImage3D&& image, BufferUsage usage);
         #endif
 
         /**
diff --git a/src/Magnum/CubeMapTextureArray.cpp b/src/Magnum/CubeMapTextureArray.cpp
index a0a8535a0..009a6acf7 100644
--- a/src/Magnum/CubeMapTextureArray.cpp
+++ b/src/Magnum/CubeMapTextureArray.cpp
@@ -78,6 +78,16 @@ BufferImage3D CubeMapTextureArray::subImage(const Int level, const Range3Di& ran
     this->subImage(level, range, image, usage);
     return std::move(image);
 }
+
+CompressedImage3D CubeMapTextureArray::compressedSubImage(const Int level, const Range3Di& range, CompressedImage3D&& image) {
+    compressedSubImage(level, range, image);
+    return std::move(image);
+}
+
+CompressedBufferImage3D CubeMapTextureArray::compressedSubImage(const Int level, const Range3Di& range, CompressedBufferImage3D&& image, const BufferUsage usage) {
+    compressedSubImage(level, range, image, usage);
+    return std::move(image);
+}
 #endif
 
 }
diff --git a/src/Magnum/CubeMapTextureArray.h b/src/Magnum/CubeMapTextureArray.h
index fc9f8f9ce..a78abb21b 100644
--- a/src/Magnum/CubeMapTextureArray.h
+++ b/src/Magnum/CubeMapTextureArray.h
@@ -526,6 +526,50 @@ class MAGNUM_EXPORT CubeMapTextureArray: public AbstractTexture {
          * @endcode
          */
         BufferImage3D subImage(Int level, const Range3Di& range, BufferImage3D&& image, BufferUsage usage);
+
+        /**
+         * @copybrief Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedImage&)
+         *
+         * See @ref Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedImage&)
+         * for more information.
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         * @requires_gl Texture image queries are not available in OpenGL ES.
+         *      See @ref Framebuffer::read() for possible workaround.
+         */
+        void compressedSubImage(Int level, const Range3Di& range, CompressedImage3D& image) {
+            AbstractTexture::compressedSubImage<3>(level, range, image);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedImage3D image = texture.compressedSubImage(0, range, {});
+         * @endcode
+         */
+        CompressedImage3D compressedSubImage(Int level, const Range3Di& range, CompressedImage3D&& image);
+
+        /**
+         * @copybrief Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedBufferImage&, BufferUsage)
+         *
+         * See @ref Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedBufferImage&, BufferUsage)
+         * for more information.
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         * @requires_gl Texture image queries are not available in OpenGL ES.
+         *      See @ref Framebuffer::read() for possible workaround.
+         */
+        void compressedSubImage(Int level, const Range3Di& range, CompressedBufferImage3D& image, BufferUsage usage) {
+            AbstractTexture::compressedSubImage<3>(level, range, image, usage);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedBufferImage3D image = texture.compressedSubImage(0, range, {}, BufferUsage::StaticRead);
+         * @endcode
+         */
+        CompressedBufferImage3D compressedSubImage(Int level, const Range3Di& range, CompressedBufferImage3D&& image, BufferUsage usage);
         #endif
 
         /**
diff --git a/src/Magnum/RectangleTexture.cpp b/src/Magnum/RectangleTexture.cpp
index 1a7b93a2b..ef516190f 100644
--- a/src/Magnum/RectangleTexture.cpp
+++ b/src/Magnum/RectangleTexture.cpp
@@ -78,5 +78,15 @@ BufferImage2D RectangleTexture::subImage(const Range2Di& range, BufferImage2D&&
     return std::move(image);
 }
 
+CompressedImage2D RectangleTexture::compressedSubImage(const Range2Di& range, CompressedImage2D&& image) {
+    compressedSubImage(range, image);
+    return std::move(image);
+}
+
+CompressedBufferImage2D RectangleTexture::compressedSubImage(const Range2Di& range, CompressedBufferImage2D&& image, const BufferUsage usage) {
+    compressedSubImage(range, image, usage);
+    return std::move(image);
+}
+
 }
 #endif
diff --git a/src/Magnum/RectangleTexture.h b/src/Magnum/RectangleTexture.h
index 186af3f70..11db9875e 100644
--- a/src/Magnum/RectangleTexture.h
+++ b/src/Magnum/RectangleTexture.h
@@ -414,6 +414,46 @@ class MAGNUM_EXPORT RectangleTexture: public AbstractTexture {
          */
         BufferImage2D subImage(const Range2Di& range, BufferImage2D&& image, BufferUsage usage);
 
+        /**
+         * @copybrief Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedImage&)
+         *
+         * See @ref Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedImage&)
+         * for more information.
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         */
+        void compressedSubImage(const Range2Di& range, CompressedImage2D& image) {
+            AbstractTexture::compressedSubImage<2>(0, range, image);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedImage2D image = texture.compressedSubImage(range, {});
+         * @endcode
+         */
+        CompressedImage2D compressedSubImage(const Range2Di& range, CompressedImage2D&& image);
+
+        /**
+         * @copybrief Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedBufferImage&, BufferUsage)
+         *
+         * See @ref Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedBufferImage&, BufferUsage)
+         * for more information.
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         */
+        void compressedSubImage(const Range2Di& range, CompressedBufferImage2D& image, BufferUsage usage) {
+            AbstractTexture::compressedSubImage<2>(0, range, image, usage);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedBufferImage2D image = texture.compressedSubImage(range, {}, BufferUsage::StaticRead);
+         * @endcode
+         */
+        CompressedBufferImage2D compressedSubImage(const Range2Di& range, CompressedBufferImage2D&& image, BufferUsage usage);
+
         /**
          * @copybrief Texture::setImage()
          * @return Reference to self (for method chaining)
diff --git a/src/Magnum/Test/CubeMapTextureArrayGLTest.cpp b/src/Magnum/Test/CubeMapTextureArrayGLTest.cpp
index e97073d02..984ee06ee 100644
--- a/src/Magnum/Test/CubeMapTextureArrayGLTest.cpp
+++ b/src/Magnum/Test/CubeMapTextureArrayGLTest.cpp
@@ -66,7 +66,9 @@ struct CubeMapTextureArrayGLTest: AbstractOpenGLTester {
     void compressedSubImageBuffer();
     #ifndef MAGNUM_TARGET_GLES
     void subImageQuery();
+    void compressedSubImageQuery();
     void subImageQueryBuffer();
+    void compressedSubImageQueryBuffer();
     #endif
 
     void generateMipmap();
@@ -109,7 +111,9 @@ CubeMapTextureArrayGLTest::CubeMapTextureArrayGLTest() {
               &CubeMapTextureArrayGLTest::compressedSubImageBuffer,
               #ifndef MAGNUM_TARGET_GLES
               &CubeMapTextureArrayGLTest::subImageQuery,
+              &CubeMapTextureArrayGLTest::compressedSubImageQuery,
               &CubeMapTextureArrayGLTest::subImageQueryBuffer,
+              &CubeMapTextureArrayGLTest::compressedSubImageQueryBuffer,
               #endif
 
               &CubeMapTextureArrayGLTest::generateMipmap,
@@ -840,6 +844,41 @@ void CubeMapTextureArrayGLTest::subImageQuery() {
         Containers::ArrayView<const UnsignedByte>{SubData}, TestSuite::Compare::Container);
 }
 
+void CubeMapTextureArrayGLTest::compressedSubImageQuery() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::texture_cube_map_array>())
+        CORRADE_SKIP(Extensions::GL::ARB::texture_cube_map_array::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_compression_s3tc>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_compression_s3tc::string() + std::string(" is not supported."));
+
+    CubeMapTextureArray texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBAS3tcDxt3, {12, 12, 6})
+        .setCompressedSubImage(0, {}, CompressedImageView3D{CompressedPixelFormat::RGBAS3tcDxt3, {12, 12, 6}, CompressedSubDataComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    /* Test also without compressed pixel storage to ensure that both size
+       computations work */
+    if(Context::current()->isExtensionSupported<Extensions::GL::ARB::compressed_texture_pixel_storage>()) {
+        CompressedImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 4, 1}, Vector3i{4}), {});
+
+        MAGNUM_VERIFY_NO_ERROR();
+
+        CORRADE_COMPARE(image.size(), Vector3i{4});
+        CORRADE_COMPARE_AS(
+            (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}),
+            Containers::ArrayView<const UnsignedByte>{CompressedSubData}, TestSuite::Compare::Container);
+    }
+
+    CompressedImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 4, 1}, Vector3i{4}), {_compressedSubDataStorage});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), Vector3i{4});
+    CORRADE_COMPARE_AS(
+        (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(_compressedSubDataOffset)),
+        Containers::ArrayView<const UnsignedByte>{CompressedSubData}, TestSuite::Compare::Container);
+}
+
 void CubeMapTextureArrayGLTest::subImageQueryBuffer() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::texture_cube_map_array>())
         CORRADE_SKIP(Extensions::GL::ARB::texture_cube_map_array::string() + std::string(" is not supported."));
@@ -862,6 +901,39 @@ void CubeMapTextureArrayGLTest::subImageQueryBuffer() {
     CORRADE_COMPARE_AS(imageData.suffix(SubDataOffset),
         Containers::ArrayView<const UnsignedByte>{SubData}, TestSuite::Compare::Container);
 }
+
+void CubeMapTextureArrayGLTest::compressedSubImageQueryBuffer() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::texture_cube_map_array>())
+        CORRADE_SKIP(Extensions::GL::ARB::texture_cube_map_array::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_compression_s3tc>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_compression_s3tc::string() + std::string(" is not supported."));
+
+    CubeMapTextureArray texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBAS3tcDxt3, {12, 12, 6})
+        .setCompressedSubImage(0, {}, CompressedImageView3D{CompressedPixelFormat::RGBAS3tcDxt3, {12, 12, 6}, CompressedSubDataComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    /* Test also without compressed pixel storage to ensure that both size
+       computations work */
+    if(Context::current()->isExtensionSupported<Extensions::GL::ARB::compressed_texture_pixel_storage>()) {
+        CompressedBufferImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 4, 1}, Vector3i{4}), {}, BufferUsage::StaticRead);
+        const auto imageData = image.buffer().data<UnsignedByte>();
+
+        MAGNUM_VERIFY_NO_ERROR();
+
+        CORRADE_COMPARE(image.size(), Vector3i{4});
+        CORRADE_COMPARE_AS(imageData, Containers::ArrayView<const UnsignedByte>{CompressedSubData}, TestSuite::Compare::Container);
+    }
+
+    CompressedBufferImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 4, 1}, Vector3i{4}), {_compressedSubDataStorage}, BufferUsage::StaticRead);
+    const auto imageData = image.buffer().data<UnsignedByte>();
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), Vector3i{4});
+    CORRADE_COMPARE_AS(imageData.suffix(_compressedSubDataOffset), Containers::ArrayView<const UnsignedByte>{CompressedSubData}, TestSuite::Compare::Container);
+}
 #endif
 
 void CubeMapTextureArrayGLTest::generateMipmap() {
diff --git a/src/Magnum/Test/CubeMapTextureGLTest.cpp b/src/Magnum/Test/CubeMapTextureGLTest.cpp
index 324f81a57..5e5534673 100644
--- a/src/Magnum/Test/CubeMapTextureGLTest.cpp
+++ b/src/Magnum/Test/CubeMapTextureGLTest.cpp
@@ -90,7 +90,9 @@ struct CubeMapTextureGLTest: AbstractOpenGLTester {
     #endif
     #ifndef MAGNUM_TARGET_GLES
     void subImageQuery();
+    void compressedSubImageQuery();
     void subImageQueryBuffer();
+    void compressedSubImageQueryBuffer();
     #endif
 
     void generateMipmap();
@@ -157,7 +159,9 @@ CubeMapTextureGLTest::CubeMapTextureGLTest() {
               #endif
               #ifndef MAGNUM_TARGET_GLES
               &CubeMapTextureGLTest::subImageQuery,
+              &CubeMapTextureGLTest::compressedSubImageQuery,
               &CubeMapTextureGLTest::subImageQueryBuffer,
+              &CubeMapTextureGLTest::compressedSubImageQueryBuffer,
               #endif
 
               &CubeMapTextureGLTest::generateMipmap,
@@ -991,6 +995,44 @@ void CubeMapTextureGLTest::subImageQuery() {
         Containers::ArrayView<const UnsignedByte>{Data}, TestSuite::Compare::Container);
 }
 
+void CubeMapTextureGLTest::compressedSubImageQuery() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
+        CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
+    /* I'm too lazy to call setSubImage() six times */
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::direct_state_access>())
+        CORRADE_SKIP(Extensions::GL::ARB::direct_state_access::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_compression_s3tc>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_compression_s3tc::string() + std::string(" is not supported."));
+
+    CubeMapTexture texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBAS3tcDxt3, Vector2i{12})
+        .setCompressedSubImage(0, {}, CompressedImageView3D{CompressedPixelFormat::RGBAS3tcDxt3, {12, 12, 1}, CompressedSubDataComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    /* Test also without compressed pixel storage to ensure that both size
+       computations work */
+    if(Context::current()->isExtensionSupported<Extensions::GL::ARB::compressed_texture_pixel_storage>()) {
+        CompressedImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 4, 0}, {4, 4, 1}), {});
+
+        MAGNUM_VERIFY_NO_ERROR();
+
+        CORRADE_COMPARE(image.size(), (Vector3i{4, 4, 1}));
+        CORRADE_COMPARE_AS(
+            (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}),
+            Containers::ArrayView<const UnsignedByte>{CompressedData}, TestSuite::Compare::Container);
+    }
+
+    CompressedImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 4, 0}, {4, 4, 1}), {_compressedDataStorage});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), (Vector3i{4, 4, 1}));
+    CORRADE_COMPARE_AS(
+        (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(_compressedDataOffset)),
+        Containers::ArrayView<const UnsignedByte>{CompressedData}, TestSuite::Compare::Container);
+}
+
 void CubeMapTextureGLTest::subImageQueryBuffer() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
         CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
@@ -1013,6 +1055,42 @@ void CubeMapTextureGLTest::subImageQueryBuffer() {
     CORRADE_COMPARE(image.size(), Vector3i(2, 2, 1));
     CORRADE_COMPARE_AS(imageData.suffix(_dataOffset), Containers::ArrayView<const UnsignedByte>{Data}, TestSuite::Compare::Container);
 }
+
+void CubeMapTextureGLTest::compressedSubImageQueryBuffer() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
+        CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
+    /* I'm too lazy to call setSubImage() six times */
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::direct_state_access>())
+        CORRADE_SKIP(Extensions::GL::ARB::direct_state_access::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_compression_s3tc>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_compression_s3tc::string() + std::string(" is not supported."));
+
+    CubeMapTexture texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBAS3tcDxt3, Vector2i{12})
+           .setCompressedSubImage(0, {}, CompressedImageView3D{CompressedPixelFormat::RGBAS3tcDxt3, {12, 12, 1}, CompressedSubDataComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    /* Test also without compressed pixel storage to ensure that both size
+       computations work */
+    if(Context::current()->isExtensionSupported<Extensions::GL::ARB::compressed_texture_pixel_storage>()) {
+        CompressedBufferImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 4, 0}, {4, 4, 1}), {}, BufferUsage::StaticRead);
+        const auto imageData = image.buffer().data<UnsignedByte>();
+
+        MAGNUM_VERIFY_NO_ERROR();
+
+        CORRADE_COMPARE(image.size(), (Vector3i{4, 4, 1}));
+        CORRADE_COMPARE_AS(imageData, Containers::ArrayView<const UnsignedByte>{CompressedData}, TestSuite::Compare::Container);
+    }
+
+    CompressedBufferImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 4, 0}, {4, 4, 1}), {_compressedDataStorage}, BufferUsage::StaticRead);
+    const auto imageData = image.buffer().data<UnsignedByte>();
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), (Vector3i{4, 4, 1}));
+    CORRADE_COMPARE_AS(imageData.suffix(_compressedDataOffset), Containers::ArrayView<const UnsignedByte>{CompressedData}, TestSuite::Compare::Container);
+}
 #endif
 
 void CubeMapTextureGLTest::generateMipmap() {
diff --git a/src/Magnum/Test/RectangleTextureGLTest.cpp b/src/Magnum/Test/RectangleTextureGLTest.cpp
index e6ea19b7a..091dee333 100644
--- a/src/Magnum/Test/RectangleTextureGLTest.cpp
+++ b/src/Magnum/Test/RectangleTextureGLTest.cpp
@@ -64,7 +64,9 @@ struct RectangleTextureGLTest: AbstractOpenGLTester {
     void subImageBuffer();
     void compressedSubImageBuffer();
     void subImageQuery();
+    void compressedSubImageQuery();
     void subImageQueryBuffer();
+    void compressedSubImageQueryBuffer();
 
     void invalidateImage();
     void invalidateSubImage();
@@ -95,7 +97,9 @@ RectangleTextureGLTest::RectangleTextureGLTest() {
               &RectangleTextureGLTest::subImageBuffer,
               &RectangleTextureGLTest::compressedSubImageBuffer,
               &RectangleTextureGLTest::subImageQuery,
+              &RectangleTextureGLTest::compressedSubImageQuery,
               &RectangleTextureGLTest::subImageQueryBuffer,
+              &RectangleTextureGLTest::compressedSubImageQueryBuffer,
 
               &RectangleTextureGLTest::invalidateImage,
               &RectangleTextureGLTest::invalidateSubImage});
@@ -398,6 +402,10 @@ void RectangleTextureGLTest::subImageQuery() {
         Containers::ArrayView<const UnsignedByte>{Data}, TestSuite::Compare::Container);
 }
 
+void RectangleTextureGLTest::compressedSubImageQuery() {
+    CORRADE_SKIP("No rectangle texture compression format exists.");
+}
+
 void RectangleTextureGLTest::subImageQueryBuffer() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::texture_rectangle>())
         CORRADE_SKIP(Extensions::GL::ARB::texture_rectangle::string() + std::string(" is not supported."));
@@ -421,6 +429,10 @@ void RectangleTextureGLTest::subImageQueryBuffer() {
         Containers::ArrayView<const UnsignedByte>{Data}, TestSuite::Compare::Container);
 }
 
+void RectangleTextureGLTest::compressedSubImageQueryBuffer() {
+    CORRADE_SKIP("No rectangle texture compression format exists.");
+}
+
 void RectangleTextureGLTest::invalidateImage() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::texture_rectangle>())
         CORRADE_SKIP(Extensions::GL::ARB::texture_rectangle::string() + std::string(" is not supported."));
diff --git a/src/Magnum/Test/TextureArrayGLTest.cpp b/src/Magnum/Test/TextureArrayGLTest.cpp
index ad79e364f..da8a88d93 100644
--- a/src/Magnum/Test/TextureArrayGLTest.cpp
+++ b/src/Magnum/Test/TextureArrayGLTest.cpp
@@ -117,7 +117,9 @@ struct TextureArrayGLTest: AbstractOpenGLTester {
     void subImage1DBuffer();
     void compressedSubImage1DBuffer();
     void subImage1DQuery();
+    void compressedSubImage1DQuery();
     void subImage1DQueryBuffer();
+    void compressedSubImage1DQueryBuffer();
     #endif
     void subImage2D();
     void compressedSubImage2D();
@@ -125,7 +127,9 @@ struct TextureArrayGLTest: AbstractOpenGLTester {
     void compressedSubImage2DBuffer();
     #ifndef MAGNUM_TARGET_GLES
     void subImage2DQuery();
+    void compressedSubImage2DQuery();
     void subImage2DQueryBuffer();
+    void compressedSubImage2DQueryBuffer();
     #endif
 
     #ifndef MAGNUM_TARGET_GLES
@@ -225,7 +229,9 @@ TextureArrayGLTest::TextureArrayGLTest() {
         &TextureArrayGLTest::subImage1DBuffer,
         &TextureArrayGLTest::compressedSubImage1DBuffer,
         &TextureArrayGLTest::subImage1DQuery,
+        &TextureArrayGLTest::compressedSubImage1DQuery,
         &TextureArrayGLTest::subImage1DQueryBuffer,
+        &TextureArrayGLTest::compressedSubImage1DQueryBuffer,
         #endif
         &TextureArrayGLTest::subImage2D,
         &TextureArrayGLTest::compressedSubImage2D,
@@ -233,7 +239,9 @@ TextureArrayGLTest::TextureArrayGLTest() {
         &TextureArrayGLTest::compressedSubImage2DBuffer,
         #ifndef MAGNUM_TARGET_GLES
         &TextureArrayGLTest::subImage2DQuery,
+        &TextureArrayGLTest::compressedSubImage2DQuery,
         &TextureArrayGLTest::subImage2DQueryBuffer,
+        &TextureArrayGLTest::compressedSubImage2DQueryBuffer,
         #endif
 
         #ifndef MAGNUM_TARGET_GLES
@@ -967,6 +975,10 @@ void TextureArrayGLTest::subImage1DQuery() {
         (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(DataOffset1D)), Containers::ArrayView<const UnsignedByte>{Data1D}, TestSuite::Compare::Container);
 }
 
+void TextureArrayGLTest::compressedSubImage1DQuery() {
+    CORRADE_SKIP("No 1D texture compression format exists.");
+}
+
 void TextureArrayGLTest::subImage1DQueryBuffer() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_array>())
         CORRADE_SKIP(Extensions::GL::EXT::texture_array::string() + std::string(" is not supported."));
@@ -989,6 +1001,10 @@ void TextureArrayGLTest::subImage1DQueryBuffer() {
     CORRADE_COMPARE_AS(imageData.suffix(DataOffset1D),
         Containers::ArrayView<const UnsignedByte>{Data1D}, TestSuite::Compare::Container);
 }
+
+void TextureArrayGLTest::compressedSubImage1DQueryBuffer() {
+    CORRADE_SKIP("No 1D texture compression format exists.");
+}
 #endif
 
 namespace {
@@ -1252,6 +1268,44 @@ void TextureArrayGLTest::subImage2DQuery() {
         (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(DataOffset2D)), Containers::ArrayView<const UnsignedByte>{Data2D}, TestSuite::Compare::Container);
 }
 
+void TextureArrayGLTest::compressedSubImage2DQuery() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_array>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_array::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
+        CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_compression_s3tc>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_compression_s3tc::string() + std::string(" is not supported."));
+
+    Texture2DArray texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBAS3tcDxt3, {12, 4, 4})
+           .setCompressedSubImage(0, {}, CompressedImageView3D{CompressedPixelFormat::RGBAS3tcDxt3,
+               {12, 4, 4}, CompressedSubData2DComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    /* Test also without compressed pixel storage to ensure that both size
+       computations work */
+    if(Context::current()->isExtensionSupported<Extensions::GL::ARB::compressed_texture_pixel_storage>()) {
+        CompressedImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 0, 1}, {4, 4, 2}), {});
+
+        MAGNUM_VERIFY_NO_ERROR();
+
+        CORRADE_COMPARE(image.size(), (Vector3i{4, 4, 2}));
+        CORRADE_COMPARE_AS(
+            (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}),
+            Containers::ArrayView<const UnsignedByte>{CompressedData2D}, TestSuite::Compare::Container);
+    }
+
+    CompressedImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 0, 1}, {4, 4, 2}), {_compressedDataStorage2D});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), (Vector3i{4, 4, 2}));
+    CORRADE_COMPARE_AS(
+        (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(_compressedDataOffset2D)),
+        Containers::ArrayView<const UnsignedByte>{CompressedData2D}, TestSuite::Compare::Container);
+}
+
 void TextureArrayGLTest::subImage2DQueryBuffer() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_array>())
         CORRADE_SKIP(Extensions::GL::EXT::texture_array::string() + std::string(" is not supported."));
@@ -1275,6 +1329,36 @@ void TextureArrayGLTest::subImage2DQueryBuffer() {
         Containers::ArrayView<const UnsignedByte>{Data2D}, TestSuite::Compare::Container);
 }
 
+void TextureArrayGLTest::compressedSubImage2DQueryBuffer() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_array>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_array::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
+        CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_compression_s3tc>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_compression_s3tc::string() + std::string(" is not supported."));
+
+    Texture2DArray texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBAS3tcDxt3, {12, 4, 4})
+           .setCompressedSubImage(0, {}, CompressedImageView3D{CompressedPixelFormat::RGBAS3tcDxt3,
+               {12, 4, 4}, CompressedSubData2DComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CompressedBufferImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 0, 1}, {4, 4, 2}), {
+        #ifndef MAGNUM_TARGET_GLES
+        _compressedDataStorage2D
+        #endif
+    }, BufferUsage::StaticRead);
+
+    MAGNUM_VERIFY_NO_ERROR();
+    const auto imageData = image.buffer().data<UnsignedByte>();
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), (Vector3i{4, 4, 2}));
+    CORRADE_COMPARE_AS(imageData.suffix(_compressedDataOffset2D), Containers::ArrayView<const UnsignedByte>{CompressedData2D}, TestSuite::Compare::Container);
+}
+
 void TextureArrayGLTest::generateMipmap1D() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::framebuffer_object>())
         CORRADE_SKIP(Extensions::GL::ARB::framebuffer_object::string() + std::string(" is not supported."));
diff --git a/src/Magnum/Test/TextureGLTest.cpp b/src/Magnum/Test/TextureGLTest.cpp
index a3918c200..3e33caa9a 100644
--- a/src/Magnum/Test/TextureGLTest.cpp
+++ b/src/Magnum/Test/TextureGLTest.cpp
@@ -139,7 +139,9 @@ struct TextureGLTest: AbstractOpenGLTester {
     void subImage1DBuffer();
     void compressedSubImage1DBuffer();
     void subImage1DQuery();
+    void compressedSubImage1DQuery();
     void subImage1DQueryBuffer();
+    void compressedSubImage1DQueryBuffer();
     #endif
     void subImage2D();
     void compressedSubImage2D();
@@ -149,7 +151,9 @@ struct TextureGLTest: AbstractOpenGLTester {
     #endif
     #ifndef MAGNUM_TARGET_GLES
     void subImage2DQuery();
+    void compressedSubImage2DQuery();
     void subImage2DQueryBuffer();
+    void compressedSubImage2DQueryBuffer();
     #endif
     void subImage3D();
     void compressedSubImage3D();
@@ -159,7 +163,9 @@ struct TextureGLTest: AbstractOpenGLTester {
     #endif
     #ifndef MAGNUM_TARGET_GLES
     void subImage3DQuery();
+    void compressedSubImage3DQuery();
     void subImage3DQueryBuffer();
+    void compressedSubImage3DQueryBuffer();
     #endif
 
     #ifndef MAGNUM_TARGET_GLES
@@ -286,7 +292,9 @@ TextureGLTest::TextureGLTest() {
         &TextureGLTest::subImage1DBuffer,
         &TextureGLTest::compressedSubImage1DBuffer,
         &TextureGLTest::subImage1DQuery,
+        &TextureGLTest::compressedSubImage1DQuery,
         &TextureGLTest::subImage1DQueryBuffer,
+        &TextureGLTest::compressedSubImage1DQueryBuffer,
         #endif
         &TextureGLTest::subImage2D,
         &TextureGLTest::compressedSubImage2D,
@@ -296,7 +304,9 @@ TextureGLTest::TextureGLTest() {
         #endif
         #ifndef MAGNUM_TARGET_GLES
         &TextureGLTest::subImage2DQuery,
+        &TextureGLTest::compressedSubImage2DQuery,
         &TextureGLTest::subImage2DQueryBuffer,
+        &TextureGLTest::compressedSubImage2DQueryBuffer,
         #endif
         &TextureGLTest::subImage3D,
         &TextureGLTest::compressedSubImage3D,
@@ -306,7 +316,9 @@ TextureGLTest::TextureGLTest() {
         #endif
         #ifndef MAGNUM_TARGET_GLES
         &TextureGLTest::subImage3DQuery,
+        &TextureGLTest::compressedSubImage3DQuery,
         &TextureGLTest::subImage3DQueryBuffer,
+        &TextureGLTest::compressedSubImage3DQueryBuffer,
         #endif
 
         #ifndef MAGNUM_TARGET_GLES
@@ -1316,6 +1328,10 @@ void TextureGLTest::subImage1DQuery() {
         (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(DataOffset1D)), Containers::ArrayView<const UnsignedByte>{Data1D}, TestSuite::Compare::Container);
 }
 
+void TextureGLTest::compressedSubImage1DQuery() {
+    CORRADE_SKIP("No 1D texture compression format exists.");
+}
+
 void TextureGLTest::subImage1DQueryBuffer() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
         CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
@@ -1336,6 +1352,10 @@ void TextureGLTest::subImage1DQueryBuffer() {
     CORRADE_COMPARE_AS(imageData.suffix(DataOffset1D),
         Containers::ArrayView<const UnsignedByte>{Data1D}, TestSuite::Compare::Container);
 }
+
+void TextureGLTest::compressedSubImage1DQueryBuffer() {
+    CORRADE_SKIP("No 1D texture compression format exists.");
+}
 #endif
 
 namespace {
@@ -1491,6 +1511,41 @@ void TextureGLTest::subImage2DQuery() {
         (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(_dataOffset2D)), Containers::ArrayView<const UnsignedByte>{Data2D}, TestSuite::Compare::Container);
 }
 
+void TextureGLTest::compressedSubImage2DQuery() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
+        CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_compression_s3tc>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_compression_s3tc::string() + std::string(" is not supported."));
+
+    Texture2D texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBAS3tcDxt3, {12, 4})
+           .setCompressedSubImage(0, {}, CompressedImageView2D{CompressedPixelFormat::RGBAS3tcDxt3, {12, 4}, CompressedSubData2DComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    /* Test also without compressed pixel storage to ensure that both size
+       computations work */
+    if(Context::current()->isExtensionSupported<Extensions::GL::ARB::compressed_texture_pixel_storage>()) {
+        CompressedImage2D image = texture.compressedSubImage(0, Range2Di::fromSize({4, 0}, Vector2i{4}), {});
+
+        MAGNUM_VERIFY_NO_ERROR();
+
+        CORRADE_COMPARE(image.size(), Vector2i{4});
+        CORRADE_COMPARE_AS(
+            (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}),
+            Containers::ArrayView<const UnsignedByte>{CompressedData2D}, TestSuite::Compare::Container);
+    }
+
+    CompressedImage2D image = texture.compressedSubImage(0, Range2Di::fromSize({4, 0}, Vector2i{4}), {_compressedDataStorage2D});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), Vector2i{4});
+    CORRADE_COMPARE_AS(
+        (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(_compressedDataOffset2D)),
+        Containers::ArrayView<const UnsignedByte>{CompressedData2D}, TestSuite::Compare::Container);
+}
+
 void TextureGLTest::subImage2DQueryBuffer() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
         CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
@@ -1511,6 +1566,39 @@ void TextureGLTest::subImage2DQueryBuffer() {
     CORRADE_COMPARE_AS(imageData.suffix(_dataOffset2D),
         Containers::ArrayView<const UnsignedByte>{Data2D}, TestSuite::Compare::Container);
 }
+
+void TextureGLTest::compressedSubImage2DQueryBuffer() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
+        CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::EXT::texture_compression_s3tc>())
+        CORRADE_SKIP(Extensions::GL::EXT::texture_compression_s3tc::string() + std::string(" is not supported."));
+
+    Texture2D texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBAS3tcDxt3, {12, 4})
+           .setCompressedSubImage(0, {}, CompressedImageView2D{CompressedPixelFormat::RGBAS3tcDxt3, {12, 4}, CompressedSubData2DComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    /* Test also without compressed pixel storage to ensure that both size
+       computations work */
+    if(Context::current()->isExtensionSupported<Extensions::GL::ARB::compressed_texture_pixel_storage>()) {
+        CompressedBufferImage2D image = texture.compressedSubImage(0, Range2Di::fromSize({4, 0}, Vector2i{4}), {}, BufferUsage::StaticRead);
+        const auto imageData = image.buffer().data<UnsignedByte>();
+
+        MAGNUM_VERIFY_NO_ERROR();
+
+        CORRADE_COMPARE(image.size(), Vector2i{4});
+        CORRADE_COMPARE_AS(imageData, Containers::ArrayView<const UnsignedByte>{CompressedData2D}, TestSuite::Compare::Container);
+    }
+
+    CompressedBufferImage2D image = texture.compressedSubImage(0, Range2Di::fromSize({4, 0}, Vector2i{4}), {_compressedDataStorage2D}, BufferUsage::StaticRead);
+    const auto imageData = image.buffer().data<UnsignedByte>();
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), Vector2i{4});
+    CORRADE_COMPARE_AS(imageData.suffix(_compressedDataOffset2D), Containers::ArrayView<const UnsignedByte>{CompressedData2D}, TestSuite::Compare::Container);
+}
 #endif
 
 namespace {
@@ -1707,6 +1795,41 @@ void TextureGLTest::subImage3DQuery() {
         (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(_dataOffset3D)), Containers::ArrayView<const UnsignedByte>{Data3D}, TestSuite::Compare::Container);
 }
 
+void TextureGLTest::compressedSubImage3DQuery() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
+        CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::texture_compression_bptc>())
+        CORRADE_SKIP(Extensions::GL::ARB::texture_compression_bptc::string() + std::string(" is not supported."));
+
+    Texture3D texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBABptcUnorm, {12, 4, 4})
+           .setCompressedSubImage(0, {}, CompressedImageView3D{CompressedPixelFormat::RGBABptcUnorm, {12, 4, 4}, CompressedSubData3DComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    /* Test also without compressed pixel storage to ensure that both size
+       computations work */
+    if(Context::current()->isExtensionSupported<Extensions::GL::ARB::compressed_texture_pixel_storage>()) {
+        CompressedImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 0, 0}, Vector3i{4}), {});
+
+        MAGNUM_VERIFY_NO_ERROR();
+
+        CORRADE_COMPARE(image.size(), (Vector3i{4}));
+        CORRADE_COMPARE_AS(
+            (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}),
+            Containers::ArrayView<const UnsignedByte>{CompressedData3D}, TestSuite::Compare::Container);
+    }
+
+    CompressedImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 0, 0}, Vector3i{4}), {_compressedDataStorage3D});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), (Vector3i{4}));
+    CORRADE_COMPARE_AS(
+        (Containers::ArrayView<const UnsignedByte>{image.data<UnsignedByte>(), image.data().size()}.suffix(_compressedDataOffset3D)),
+        Containers::ArrayView<const UnsignedByte>{CompressedData3D}, TestSuite::Compare::Container);
+}
+
 void TextureGLTest::subImage3DQueryBuffer() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
         CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
@@ -1728,6 +1851,39 @@ void TextureGLTest::subImage3DQueryBuffer() {
         Containers::ArrayView<const UnsignedByte>{Data3D}, TestSuite::Compare::Container);
 }
 
+void TextureGLTest::compressedSubImage3DQueryBuffer() {
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::get_texture_sub_image>())
+        CORRADE_SKIP(Extensions::GL::ARB::get_texture_sub_image::string() + std::string(" is not supported."));
+    if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::texture_compression_bptc>())
+        CORRADE_SKIP(Extensions::GL::ARB::texture_compression_bptc::string() + std::string(" is not supported."));
+
+    Texture3D texture;
+    texture.setStorage(1, TextureFormat::CompressedRGBABptcUnorm, {12, 4, 4})
+           .setCompressedSubImage(0, {}, CompressedImageView3D{CompressedPixelFormat::RGBABptcUnorm, {12, 4, 4}, CompressedSubData3DComplete});
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    /* Test also without compressed pixel storage to ensure that both size
+       computations work */
+    if(Context::current()->isExtensionSupported<Extensions::GL::ARB::compressed_texture_pixel_storage>()) {
+        CompressedBufferImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 0, 0}, Vector3i{4}), {}, BufferUsage::StaticRead);
+        const auto imageData = image.buffer().data<UnsignedByte>();
+
+        MAGNUM_VERIFY_NO_ERROR();
+
+        CORRADE_COMPARE(image.size(), Vector3i{4});
+        CORRADE_COMPARE_AS(imageData, Containers::ArrayView<const UnsignedByte>{CompressedData3D}, TestSuite::Compare::Container);
+    }
+
+    CompressedBufferImage3D image = texture.compressedSubImage(0, Range3Di::fromSize({4, 0, 0}, Vector3i{4}), {_compressedDataStorage3D}, BufferUsage::StaticRead);
+    const auto imageData = image.buffer().data<UnsignedByte>();
+
+    MAGNUM_VERIFY_NO_ERROR();
+
+    CORRADE_COMPARE(image.size(), Vector3i{4});
+    CORRADE_COMPARE_AS(imageData.suffix(_compressedDataOffset3D), Containers::ArrayView<const UnsignedByte>{CompressedData3D}, TestSuite::Compare::Container);
+}
+
 void TextureGLTest::generateMipmap1D() {
     if(!Context::current()->isExtensionSupported<Extensions::GL::ARB::framebuffer_object>())
         CORRADE_SKIP(Extensions::GL::ARB::framebuffer_object::string() + std::string(" is not supported."));
diff --git a/src/Magnum/Texture.cpp b/src/Magnum/Texture.cpp
index 018d8084b..db9553812 100644
--- a/src/Magnum/Texture.cpp
+++ b/src/Magnum/Texture.cpp
@@ -93,6 +93,16 @@ template<UnsignedInt dimensions> BufferImage<dimensions> Texture<dimensions>::su
     return std::move(image);
 }
 
+template<UnsignedInt dimensions> CompressedImage<dimensions> Texture<dimensions>::compressedSubImage(const Int level, const RangeTypeFor<dimensions, Int>& range, CompressedImage<dimensions>&& image) {
+    compressedSubImage(level, range, image);
+    return std::move(image);
+}
+
+template<UnsignedInt dimensions> CompressedBufferImage<dimensions> Texture<dimensions>::compressedSubImage(const Int level, const RangeTypeFor<dimensions, Int>& range, CompressedBufferImage<dimensions>&& image, const BufferUsage usage) {
+    compressedSubImage(level, range, image, usage);
+    return std::move(image);
+}
+
 template class MAGNUM_EXPORT Texture<1>;
 template class MAGNUM_EXPORT Texture<2>;
 template class MAGNUM_EXPORT Texture<3>;
diff --git a/src/Magnum/Texture.h b/src/Magnum/Texture.h
index 288b0189a..c99773547 100644
--- a/src/Magnum/Texture.h
+++ b/src/Magnum/Texture.h
@@ -860,6 +860,61 @@ template<UnsignedInt dimensions> class Texture: public AbstractTexture {
          * @endcode
          */
         BufferImage<dimensions> subImage(Int level, const RangeTypeFor<dimensions, Int>& range, BufferImage<dimensions>&& image, BufferUsage usage);
+
+        /**
+         * @brief Read range of given compressed texture mip level to image
+         * @param level             Mip level
+         * @param range             Range to read
+         * @param image             Image where to put the compressed data
+         *
+         * Compression format and data size are taken from the texture.
+         * @see @fn_gl2{GetTextureLevelParameter,GetTexLevelParameter},
+         *      @fn_gl_extension{GetTextureLevelParameter,EXT,direct_state_access},
+         *      eventually @fn_gl{GetTexLevelParameter} with
+         *      @def_gl{TEXTURE_COMPRESSED_IMAGE_SIZE}, @def_gl{TEXTURE_INTERNAL_FORMAT},
+         *      then @fn_gl{GetCompressedTextureSubImage}
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         * @requires_gl Texture image queries are not available in OpenGL ES or
+         *      WebGL. See @ref Framebuffer::read() for possible workaround.
+         */
+        void compressedSubImage(Int level, const RangeTypeFor<dimensions, Int>& range, CompressedImage<dimensions>& image) {
+            AbstractTexture::compressedSubImage<dimensions>(level, range, image);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedImage2D image = texture.compressedSubImage(0, rect, {});
+         * @endcode
+         */
+        CompressedImage<dimensions> compressedSubImage(Int level, const RangeTypeFor<dimensions, Int>& range, CompressedImage<dimensions>&& image);
+
+        /**
+         * @brief Read range of given compressed texture mip level to buffer image
+         * @param level             Mip level
+         * @param range             Range to read
+         * @param image             Buffer image where to put the compressed data
+         * @param usage             Buffer usage
+         *
+         * See @ref compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedBufferImage&, BufferUsage)
+         * for more information.
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         * @requires_gl Texture image queries are not available in OpenGL ES or
+         *      WebGL. See @ref Framebuffer::read() for possible workaround.
+         */
+        void compressedSubImage(Int level, const RangeTypeFor<dimensions, Int>& range, CompressedBufferImage<dimensions>& image, BufferUsage usage) {
+            AbstractTexture::compressedSubImage<dimensions>(level, range, image, usage);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedBufferImage2D image = texture.compressedSubImage(0, rect, {}, BufferUsage::StaticRead);
+         * @endcode
+         */
+        CompressedBufferImage<dimensions> compressedSubImage(Int level, const RangeTypeFor<dimensions, Int>& range, CompressedBufferImage<dimensions>&& image, BufferUsage usage);
         #endif
 
         /**
diff --git a/src/Magnum/TextureArray.cpp b/src/Magnum/TextureArray.cpp
index de611004f..e30f6cd6a 100644
--- a/src/Magnum/TextureArray.cpp
+++ b/src/Magnum/TextureArray.cpp
@@ -84,6 +84,16 @@ template<UnsignedInt dimensions> BufferImage<dimensions+1> TextureArray<dimensio
     this->subImage(level, range, image, usage);
     return std::move(image);
 }
+
+template<UnsignedInt dimensions> CompressedImage<dimensions+1> TextureArray<dimensions>::compressedSubImage(const Int level, const RangeTypeFor<dimensions+1, Int>& range, CompressedImage<dimensions+1>&& image) {
+    compressedSubImage(level, range, image);
+    return std::move(image);
+}
+
+template<UnsignedInt dimensions> CompressedBufferImage<dimensions+1> TextureArray<dimensions>::compressedSubImage(const Int level, const RangeTypeFor<dimensions+1, Int>& range, CompressedBufferImage<dimensions+1>&& image, const BufferUsage usage) {
+    compressedSubImage(level, range, image, usage);
+    return std::move(image);
+}
 #endif
 
 #ifndef MAGNUM_TARGET_GLES
diff --git a/src/Magnum/TextureArray.h b/src/Magnum/TextureArray.h
index a61370ed4..d0f7498f2 100644
--- a/src/Magnum/TextureArray.h
+++ b/src/Magnum/TextureArray.h
@@ -551,6 +551,50 @@ template<UnsignedInt dimensions> class TextureArray: public AbstractTexture {
          * @endcode
          */
         BufferImage<dimensions+1> subImage(Int level, const RangeTypeFor<dimensions+1, Int>& range, BufferImage<dimensions+1>&& image, BufferUsage usage);
+
+        /**
+         * @copybrief Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedImage&)
+         *
+         * See @ref Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedImage&)
+         * for more information.
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         * @requires_gl Texture image queries are not available in OpenGL ES or
+         *      WebGL. See @ref Framebuffer::read() for possible workaround.
+         */
+        void compressedSubImage(Int level, const RangeTypeFor<dimensions+1, Int>& range, CompressedImage<dimensions+1>& image) {
+            AbstractTexture::compressedSubImage<dimensions+1>(level, range, image);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedImage3D image = texture.compressedSubImage(0, range, {});
+         * @endcode
+         */
+        CompressedImage<dimensions+1> compressedSubImage(Int level, const RangeTypeFor<dimensions+1, Int>& range, CompressedImage<dimensions+1>&& image);
+
+        /**
+         * @copybrief Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedBufferImage&, BufferUsage)
+         *
+         * See @ref Texture::compressedSubImage(Int, const RangeTypeFor<dimensions, Int>&, CompressedBufferImage&, BufferUsage)
+         * for more information.
+         * @requires_gl45 Extension @extension{ARB,get_texture_sub_image}
+         * @requires_gl Texture image queries are not available in OpenGL ES or
+         *      WebGL. See @ref Framebuffer::read() for possible workaround.
+         */
+        void compressedSubImage(Int level, const RangeTypeFor<dimensions+1, Int>& range, CompressedBufferImage<dimensions+1>& image, BufferUsage usage) {
+            AbstractTexture::compressedSubImage<dimensions+1>(level, range, image, usage);
+        }
+
+        /** @overload
+         *
+         * Convenience alternative to the above, example usage:
+         * @code
+         * CompressedBufferImage3D image = texture.compressedSubImage(0, range, {}, BufferUsage::StaticRead);
+         * @endcode
+         */
+        CompressedBufferImage<dimensions+1> compressedSubImage(Int level, const RangeTypeFor<dimensions+1, Int>& range, CompressedBufferImage<dimensions+1>&& image, BufferUsage usage);
         #endif
 
         /**