diff --git a/doc/changelog.dox b/doc/changelog.dox
index 8413fedb1..0a216a322 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -606,6 +606,11 @@ See also:
     in @ref GL::Extensions for compatibility with older browsers.
 -   Re-enabled @fn_gl{DrawRangeElements} for WebGL 2, this time hopefully for
     the last time (see [mosra/magnum#97](https://github.com/mosra/magnum/issues/97))
+-   Added @ref GL::genericPixelFormat() and
+    @ref GL::genericCompressedPixelFormat() helpers for convenient mapping of
+    @ref GL::PixelFormat, @ref GL::PixelType, @ref GL::CompressedPixelFormat
+    and @ref GL::TextureFormat values back to the generic @ref PixelFormat and
+    @ref CompressedPixelFormat
 
 @subsubsection changelog-latest-changes-math Math library
 
diff --git a/src/Magnum/DebugTools/Screenshot.cpp b/src/Magnum/DebugTools/Screenshot.cpp
index c74fa9327..d6d034788 100644
--- a/src/Magnum/DebugTools/Screenshot.cpp
+++ b/src/Magnum/DebugTools/Screenshot.cpp
@@ -47,20 +47,9 @@ bool screenshot(PluginManager::Manager<Trade::AbstractImageConverter>& manager,
     /* Get the implementation-specific color read format for given framebuffer */
     const GL::PixelFormat format = framebuffer.implementationColorReadFormat();
     const GL::PixelType type = framebuffer.implementationColorReadType();
-    auto genericFormat = [](GL::PixelFormat format, GL::PixelType type) -> Containers::Optional<PixelFormat> {
-        #ifndef DOXYGEN_GENERATING_OUTPUT /* It gets *really* confused */
-        #define _c(generic, glFormat, glType, glTextureFormat) if(format == GL::PixelFormat::glFormat && type == GL::PixelType::glType) return PixelFormat::generic;
-        #define _n(generic, glFormat, glType) if(format == GL::PixelFormat::glFormat && type == GL::PixelType::glType) return PixelFormat::generic;
-        #define _s(generic) return {};
-        #include "Magnum/GL/Implementation/pixelFormatMapping.hpp"
-        #undef _c
-        #undef _n
-        #undef _s
-        #endif
-        return {};
-    }(format, type);
+    const Containers::Optional<PixelFormat> genericFormat = GL::genericPixelFormat(format, type);
     if(!genericFormat) {
-        Error{} << "DebugTools::screenshot(): can't map (" << Debug::nospace << format << Debug::nospace << "," << type << Debug::nospace << ") to a generic pixel format";
+        Error{} << "DebugTools::screenshot(): can't map {" << Debug::nospace << format << Debug::nospace << "," << type << Debug::nospace << "} to a generic pixel format";
         return false;
     }
 
diff --git a/src/Magnum/DebugTools/Test/ScreenshotGLTest.cpp b/src/Magnum/DebugTools/Test/ScreenshotGLTest.cpp
index 479b82798..4b4d590a7 100644
--- a/src/Magnum/DebugTools/Test/ScreenshotGLTest.cpp
+++ b/src/Magnum/DebugTools/Test/ScreenshotGLTest.cpp
@@ -244,9 +244,9 @@ void ScreenshotGLTest::unknownFormat() {
     CORRADE_VERIFY(!succeeded);
 
     if(framebuffer.implementationColorReadFormat() == GL::PixelFormat::RGBA)
-        CORRADE_COMPARE(out.str(), "DebugTools::screenshot(): can't map (GL::PixelFormat::RGBA, GL::PixelType::UnsignedShort565) to a generic pixel format\n");
+        CORRADE_COMPARE(out.str(), "DebugTools::screenshot(): can't map {GL::PixelFormat::RGBA, GL::PixelType::UnsignedShort565} to a generic pixel format\n");
     else
-        CORRADE_COMPARE(out.str(), "DebugTools::screenshot(): can't map (GL::PixelFormat::RGB, GL::PixelType::UnsignedShort565) to a generic pixel format\n");
+        CORRADE_COMPARE(out.str(), "DebugTools::screenshot(): can't map {GL::PixelFormat::RGB, GL::PixelType::UnsignedShort565} to a generic pixel format\n");
 }
 
 void ScreenshotGLTest::pluginLoadFailed() {
diff --git a/src/Magnum/GL/Implementation/compressedPixelFormatMapping.hpp b/src/Magnum/GL/Implementation/compressedPixelFormatMapping.hpp
index 043da4799..2d5f5931b 100644
--- a/src/Magnum/GL/Implementation/compressedPixelFormatMapping.hpp
+++ b/src/Magnum/GL/Implementation/compressedPixelFormatMapping.hpp
@@ -23,7 +23,11 @@
     DEALINGS IN THE SOFTWARE.
 */
 
-/* See Magnum/GL/PixelFormat.cpp and Magnum/GL/Test/PixelFormatTest.cpp */
+/* See Magnum/GL/PixelFormat.cpp and Magnum/GL/Test/PixelFormatTest.cpp. _c()
+   is a mapping with the second element being both a CompressedPixelFormat and
+   a (compressed) TextureFormat as they share the same values. _s() denotes a
+   skipped value (so the enum numbering is preserved), _d() denotes a duplicate
+   _c() value, i.e. a N:1 mapping from a generic format. */
 #ifdef _c
 _c(Bc1RGBUnorm, RGBS3tcDxt1)
 _c(Bc1RGBSrgb, SRGBS3tcDxt1)
@@ -62,77 +66,77 @@ _c(Etc2RGB8A1Unorm, RGB8PunchthroughAlpha1Etc2)
 _c(Etc2RGB8A1Srgb, SRGB8PunchthroughAlpha1Etc2)
 _c(Etc2RGBA8Unorm, RGBA8Etc2Eac)
 _c(Etc2RGBA8Srgb, SRGB8Alpha8Etc2Eac)
-_c(Astc4x4RGBAUnorm, RGBAAstc4x4)
+_d(Astc4x4RGBAUnorm, RGBAAstc4x4)
 _c(Astc4x4RGBASrgb, SRGB8Alpha8Astc4x4)
 _c(Astc4x4RGBAF, RGBAAstc4x4)
-_c(Astc5x4RGBAUnorm, RGBAAstc5x4)
+_d(Astc5x4RGBAUnorm, RGBAAstc5x4)
 _c(Astc5x4RGBASrgb, SRGB8Alpha8Astc5x4)
 _c(Astc5x4RGBAF, RGBAAstc5x4)
-_c(Astc5x5RGBAUnorm, RGBAAstc5x5)
+_d(Astc5x5RGBAUnorm, RGBAAstc5x5)
 _c(Astc5x5RGBASrgb, SRGB8Alpha8Astc5x5)
 _c(Astc5x5RGBAF, RGBAAstc5x5)
-_c(Astc6x5RGBAUnorm, RGBAAstc6x5)
+_d(Astc6x5RGBAUnorm, RGBAAstc6x5)
 _c(Astc6x5RGBASrgb, SRGB8Alpha8Astc6x5)
 _c(Astc6x5RGBAF, RGBAAstc6x5)
-_c(Astc6x6RGBAUnorm, RGBAAstc6x6)
+_d(Astc6x6RGBAUnorm, RGBAAstc6x6)
 _c(Astc6x6RGBASrgb, SRGB8Alpha8Astc6x6)
 _c(Astc6x6RGBAF, RGBAAstc6x6)
-_c(Astc8x5RGBAUnorm, RGBAAstc8x5)
+_d(Astc8x5RGBAUnorm, RGBAAstc8x5)
 _c(Astc8x5RGBASrgb, SRGB8Alpha8Astc8x5)
 _c(Astc8x5RGBAF, RGBAAstc8x5)
-_c(Astc8x6RGBAUnorm, RGBAAstc8x6)
+_d(Astc8x6RGBAUnorm, RGBAAstc8x6)
 _c(Astc8x6RGBASrgb, SRGB8Alpha8Astc8x6)
 _c(Astc8x6RGBAF, RGBAAstc8x6)
-_c(Astc8x8RGBAUnorm, RGBAAstc8x8)
+_d(Astc8x8RGBAUnorm, RGBAAstc8x8)
 _c(Astc8x8RGBASrgb, SRGB8Alpha8Astc8x8)
 _c(Astc8x8RGBAF, RGBAAstc8x8)
-_c(Astc10x5RGBAUnorm, RGBAAstc10x5)
+_d(Astc10x5RGBAUnorm, RGBAAstc10x5)
 _c(Astc10x5RGBASrgb, SRGB8Alpha8Astc10x5)
 _c(Astc10x5RGBAF, RGBAAstc10x5)
-_c(Astc10x6RGBAUnorm, RGBAAstc10x6)
+_d(Astc10x6RGBAUnorm, RGBAAstc10x6)
 _c(Astc10x6RGBASrgb, SRGB8Alpha8Astc10x6)
 _c(Astc10x6RGBAF, RGBAAstc10x6)
-_c(Astc10x8RGBAUnorm, RGBAAstc10x8)
+_d(Astc10x8RGBAUnorm, RGBAAstc10x8)
 _c(Astc10x8RGBASrgb, SRGB8Alpha8Astc10x8)
 _c(Astc10x8RGBAF, RGBAAstc10x8)
-_c(Astc10x10RGBAUnorm, RGBAAstc10x10)
+_d(Astc10x10RGBAUnorm, RGBAAstc10x10)
 _c(Astc10x10RGBASrgb, SRGB8Alpha8Astc10x10)
 _c(Astc10x10RGBAF, RGBAAstc10x10)
-_c(Astc12x10RGBAUnorm, RGBAAstc12x10)
+_d(Astc12x10RGBAUnorm, RGBAAstc12x10)
 _c(Astc12x10RGBASrgb, SRGB8Alpha8Astc12x10)
 _c(Astc12x10RGBAF, RGBAAstc12x10)
-_c(Astc12x12RGBAUnorm, RGBAAstc12x12)
+_d(Astc12x12RGBAUnorm, RGBAAstc12x12)
 _c(Astc12x12RGBASrgb, SRGB8Alpha8Astc12x12)
 _c(Astc12x12RGBAF, RGBAAstc12x12)
 #if defined(MAGNUM_TARGET_GLES) && !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
-_c(Astc3x3x3RGBAUnorm, RGBAAstc3x3x3)
+_d(Astc3x3x3RGBAUnorm, RGBAAstc3x3x3)
 _c(Astc3x3x3RGBASrgb, SRGB8Alpha8Astc3x3x3)
 _c(Astc3x3x3RGBAF, RGBAAstc3x3x3)
-_c(Astc4x3x3RGBAUnorm, RGBAAstc4x3x3)
+_d(Astc4x3x3RGBAUnorm, RGBAAstc4x3x3)
 _c(Astc4x3x3RGBASrgb, SRGB8Alpha8Astc4x3x3)
 _c(Astc4x3x3RGBAF, RGBAAstc4x3x3)
-_c(Astc4x4x3RGBAUnorm, RGBAAstc4x4x3)
+_d(Astc4x4x3RGBAUnorm, RGBAAstc4x4x3)
 _c(Astc4x4x3RGBASrgb, SRGB8Alpha8Astc4x4x3)
 _c(Astc4x4x3RGBAF, RGBAAstc4x4x3)
-_c(Astc4x4x4RGBAUnorm, RGBAAstc4x4x4)
+_d(Astc4x4x4RGBAUnorm, RGBAAstc4x4x4)
 _c(Astc4x4x4RGBASrgb, SRGB8Alpha8Astc4x4x4)
 _c(Astc4x4x4RGBAF, RGBAAstc4x4x4)
-_c(Astc5x4x4RGBAUnorm, RGBAAstc5x4x4)
+_d(Astc5x4x4RGBAUnorm, RGBAAstc5x4x4)
 _c(Astc5x4x4RGBASrgb, SRGB8Alpha8Astc5x4x4)
 _c(Astc5x4x4RGBAF, RGBAAstc5x4x4)
-_c(Astc5x5x4RGBAUnorm, RGBAAstc5x5x4)
+_d(Astc5x5x4RGBAUnorm, RGBAAstc5x5x4)
 _c(Astc5x5x4RGBASrgb, SRGB8Alpha8Astc5x5x4)
 _c(Astc5x5x4RGBAF, RGBAAstc5x5x4)
-_c(Astc5x5x5RGBAUnorm, RGBAAstc5x5x5)
+_d(Astc5x5x5RGBAUnorm, RGBAAstc5x5x5)
 _c(Astc5x5x5RGBASrgb, SRGB8Alpha8Astc5x5x5)
 _c(Astc5x5x5RGBAF, RGBAAstc5x5x5)
-_c(Astc6x5x5RGBAUnorm, RGBAAstc6x5x5)
+_d(Astc6x5x5RGBAUnorm, RGBAAstc6x5x5)
 _c(Astc6x5x5RGBASrgb, SRGB8Alpha8Astc6x5x5)
 _c(Astc6x5x5RGBAF, RGBAAstc6x5x5)
-_c(Astc6x6x5RGBAUnorm, RGBAAstc6x6x5)
+_d(Astc6x6x5RGBAUnorm, RGBAAstc6x6x5)
 _c(Astc6x6x5RGBASrgb, SRGB8Alpha8Astc6x6x5)
 _c(Astc6x6x5RGBAF, RGBAAstc6x6x5)
-_c(Astc6x6x6RGBAUnorm, RGBAAstc6x6x6)
+_d(Astc6x6x6RGBAUnorm, RGBAAstc6x6x6)
 _c(Astc6x6x6RGBASrgb, SRGB8Alpha8Astc6x6x6)
 _c(Astc6x6x6RGBAF, RGBAAstc6x6x6)
 #else
diff --git a/src/Magnum/GL/Implementation/pixelFormatMapping.hpp b/src/Magnum/GL/Implementation/pixelFormatMapping.hpp
index 1fea0520a..c55504dbf 100644
--- a/src/Magnum/GL/Implementation/pixelFormatMapping.hpp
+++ b/src/Magnum/GL/Implementation/pixelFormatMapping.hpp
@@ -26,7 +26,10 @@
 /* See Magnum/GL/PixelFormat.cpp, Magnum/GL/Test/PixelFormatTest.cpp and
    DebugTools/Screenshot.cpp. _c() is a mapping, _s() denotes a skipped value
    (so the enum numbering is preserved), _n() denotes a value where pixel
-   format mapping is defined, but texture format is not */
+   format mapping is defined, but texture format is not; _d() denotes a
+   _c() value with duplicated format/type combination, i.e. a N:1 mapping from
+   a generic format, _dn() then a _n() value with duplicated format/type
+   combination. */
 #ifdef _c
 #ifndef MAGNUM_TARGET_GLES2
 _c(R8Unorm, Red, UnsignedByte, R8)
@@ -58,23 +61,26 @@ _s(RGBA8Snorm)
    texture format tho. */
 #ifndef MAGNUM_TARGET_GLES2
 #ifndef MAGNUM_TARGET_WEBGL
-_c(R8Srgb, Red, UnsignedByte, SR8)
-_c(RG8Srgb, RG, UnsignedByte, SRG8)
+_d(R8Srgb, Red, UnsignedByte, SR8)
+_d(RG8Srgb, RG, UnsignedByte, SRG8)
 #else
-_n(R8Srgb, Red, UnsignedByte)
-_n(RG8Srgb, RG, UnsignedByte)
+_dn(R8Srgb, Red, UnsignedByte)
+_dn(RG8Srgb, RG, UnsignedByte)
 #endif
 #else
 /* SLUMINANCE / SLUMINANCE_ALPHA texture formats not exposed */
-_n(R8Srgb, Luminance, UnsignedByte)
-_n(RG8Srgb, LuminanceAlpha, UnsignedByte)
+_dn(R8Srgb, Luminance, UnsignedByte)
+_dn(RG8Srgb, LuminanceAlpha, UnsignedByte)
 #endif
+/* Again, GL's pixel format doesn't distinguish between linear and sRGB, so
+   mapping is the same as in case of the Unorm types. It's encoded in the
+   texture format tho. */
 #ifndef MAGNUM_TARGET_GLES2
-_c(RGB8Srgb, RGB, UnsignedByte, SRGB8)
-_c(RGBA8Srgb, RGBA, UnsignedByte, SRGB8Alpha8)
+_d(RGB8Srgb, RGB, UnsignedByte, SRGB8)
+_d(RGBA8Srgb, RGBA, UnsignedByte, SRGB8Alpha8)
 #else
-_n(RGB8Srgb, RGB, UnsignedByte)
-_n(RGBA8Srgb, RGBA, UnsignedByte)
+_dn(RGB8Srgb, RGB, UnsignedByte)
+_dn(RGBA8Srgb, RGBA, UnsignedByte)
 #endif
 #ifndef MAGNUM_TARGET_GLES2
 _c(R8UI, RedInteger, UnsignedByte, R8UI)
diff --git a/src/Magnum/GL/PixelFormat.cpp b/src/Magnum/GL/PixelFormat.cpp
index b21a215cd..e7ddc365d 100644
--- a/src/Magnum/GL/PixelFormat.cpp
+++ b/src/Magnum/GL/PixelFormat.cpp
@@ -25,8 +25,9 @@
 
 #include "PixelFormat.h"
 
-#include <Corrade/Utility/Assert.h>
 #include <Corrade/Containers/ArrayView.h>
+#include <Corrade/Containers/Optional.h>
+#include <Corrade/Utility/Assert.h>
 #include <Corrade/Utility/Debug.h>
 
 #include "Magnum/PixelFormat.h"
@@ -41,24 +42,32 @@ constexpr struct {
     PixelFormat format;
     PixelType type;
 } FormatMapping[] {
-    #define _c(input, format, type, textureFormat) {PixelFormat::format, PixelType::type},
-    /* GCC 4.8 doesn't like just a {} for default enum values */
     #define _n(input, format, type) {PixelFormat::format, PixelType::type},
+    #define _dn _n
+    #define _c(input, format, type, textureFormat) _n(input, format, type)
+    #define _d _c
+    /* GCC 4.8 doesn't like just a {} for default enum values */
     #define _s(input) {PixelFormat{}, PixelType{}},
     #include "Magnum/GL/Implementation/pixelFormatMapping.hpp"
     #undef _s
-    #undef _n
+    #undef _d
     #undef _c
+    #undef _nd
+    #undef _n
 };
 
 constexpr TextureFormat TextureFormatMapping[] {
     #define _c(input, format, type, textureFormat) TextureFormat::textureFormat,
+    #define _d _c
     /* GCC 4.8 doesn't like just a {} for default enum values */
-    #define _n(input, format, type) TextureFormat{},
     #define _s(input) TextureFormat{},
+    #define _n(input, format, type) _s(input)
+    #define _dn _n
     #include "Magnum/GL/Implementation/pixelFormatMapping.hpp"
-    #undef _s
+    #undef _dn
     #undef _n
+    #undef _s
+    #undef _d
     #undef _c
 };
 #endif
@@ -261,6 +270,57 @@ UnsignedInt pixelFormatSize(const PixelFormat format, const PixelType type) {
     CORRADE_INTERNAL_ASSERT_UNREACHABLE(); /* LCOV_EXCL_LINE */
 }
 
+Containers::Optional<Magnum::PixelFormat> genericPixelFormat(const PixelFormat format, PixelType type) {
+    /* Assuming a switch will get better optimized to some LUT than an if
+       cascade */
+    switch((UnsignedLong(format) << 32)|UnsignedLong(type)) {
+        #define _n(input, format, type)                                     \
+            case (UnsignedLong(PixelFormat::format) << 32)|                 \
+                  UnsignedLong(PixelType::type):                            \
+                return Magnum::PixelFormat::input;
+        #define _c(input, format, type, textureFormat) _n(input, format, type)
+        #define _d(input, format, type, textureFormat)
+        #define _dn(input, format, type)
+        #define _s(input)
+        #include "Magnum/GL/Implementation/pixelFormatMapping.hpp"
+        #undef _s
+        #undef _dn
+        #undef _n
+        #undef _d
+        #undef _c
+    }
+
+    return {};
+}
+
+Containers::Optional<Magnum::PixelFormat> genericPixelFormat(const TextureFormat format) {
+    switch(format) {
+        #define _c(input, format, type, textureFormat)                      \
+            case TextureFormat::textureFormat: return Magnum::PixelFormat::input;
+        #define _d _c
+        #define _n(input, format, type)
+        #define _dn(input, format, type)
+        #define _s(input)
+        #include "Magnum/GL/Implementation/pixelFormatMapping.hpp"
+        #undef _s
+        #undef _dn
+        #undef _n
+        #undef _d
+        #undef _c
+
+        /* For compressed formats it returns NullOpt too instead of asserting,
+           as -- compared to the generic-to-GL translation, which is O(1) --
+           the inverse mapping is potentially a linear lookup and forcing the
+           user to check some isTextureFormatCompressed() first (which would do
+           another linear lookup) makes no sense from a perf PoV. Plus for
+           unknown formats it's unknown whether it's a compressed format or
+           not, and the function suddenly starting to assert when a format
+           becomes known isn't good for backwards compatibility. */
+        default:
+            return {};
+    }
+}
+
 #ifndef DOXYGEN_GENERATING_OUTPUT
 Debug& operator<<(Debug& debug, const PixelFormat value) {
     debug << "GL::PixelFormat" << Debug::nospace;
@@ -402,9 +462,11 @@ namespace {
    having just a single table for both */
 constexpr CompressedPixelFormat CompressedFormatMapping[] {
     #define _c(input, format) CompressedPixelFormat::format,
+    #define _d _c
     #define _s(input) CompressedPixelFormat{},
     #include "Magnum/GL/Implementation/compressedPixelFormatMapping.hpp"
     #undef _s
+    #undef _d
     #undef _c
 };
 #endif
@@ -455,6 +517,38 @@ TextureFormat textureFormat(const Magnum::CompressedPixelFormat format) {
     return out;
 }
 
+Containers::Optional<Magnum::CompressedPixelFormat> genericCompressedPixelFormat(const CompressedPixelFormat format) {
+    switch(format) {
+        #define _c(input, format)                                           \
+            case CompressedPixelFormat::format:                             \
+                return Magnum::CompressedPixelFormat::input;
+        #define _d(input, format)
+        #define _s(input)
+        #include "Magnum/GL/Implementation/compressedPixelFormatMapping.hpp"
+        #undef _s
+        #undef _d
+        #undef _c
+
+        default:
+            return {};
+    }
+}
+
+Containers::Optional<Magnum::CompressedPixelFormat> genericCompressedPixelFormat(const TextureFormat format) {
+    /* Enum values are the same between CompressedPixelFormat and
+       TextureFormat, so just casting and delegating.
+
+       For uncompressed formats it returns NullOpt too instead of asserting, as
+       -- compared to the generic-to-GL translation, which is O(1) -- the
+       inverse mapping is potentially a linear lookup and forcing the user to
+       check some isTextureFormatCompressed() first (which would do another
+       linear lookup) makes no sense from a perf PoV. Plus for unknown formats
+       it's unknown whether it's a compressed format or not, and the function
+       suddenly starting to assert when a format becomes known isn't good for
+       backwards compatibility. */
+    return genericCompressedPixelFormat(CompressedPixelFormat(UnsignedInt(format)));
+}
+
 Debug& operator<<(Debug& debug, const CompressedPixelFormat value) {
     debug << "GL::CompressedPixelFormat" << Debug::nospace;
 
diff --git a/src/Magnum/GL/PixelFormat.h b/src/Magnum/GL/PixelFormat.h
index 487f9c8ad..e782a1ea4 100644
--- a/src/Magnum/GL/PixelFormat.h
+++ b/src/Magnum/GL/PixelFormat.h
@@ -26,7 +26,7 @@
 */
 
 /** @file
- * @brief Enum @ref Magnum::GL::PixelFormat, @ref Magnum::GL::PixelType, @ref Magnum::GL::CompressedPixelFormat, function @ref Magnum::GL::hasPixelFormat(), @ref Magnum::GL::pixelFormat(), @ref Magnum::GL::pixelType(), @ref Magnum::GL::pixelFormatSize(), @ref Magnum::GL::hasCompressedPixelFormat(), @ref Magnum::GL::compressedPixelFormat()
+ * @brief Enum @ref Magnum::GL::PixelFormat, @ref Magnum::GL::PixelType, @ref Magnum::GL::CompressedPixelFormat, function @ref Magnum::GL::hasPixelFormat(), @ref Magnum::GL::pixelFormat(), @ref Magnum::GL::pixelType(), @ref Magnum::GL::pixelFormatSize(), @ref Magnum::GL::genericPixelFormat(), @ref Magnum::GL::hasCompressedPixelFormat(), @ref Magnum::GL::compressedPixelFormat(), @ref Magnum::GL::genericCompressedPixelFormat()
  */
 
 #include <Corrade/Utility/Assert.h>
@@ -648,6 +648,7 @@ value is expected to be valid.
     extension. Such check is outside of the scope of this function and you are
     expected to verify extension availability before using such format.
 
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
 @see @ref pixelFormat(), @ref pixelType(), @ref hasCompressedPixelFormat()
 */
 MAGNUM_GL_EXPORT bool hasPixelFormat(Magnum::PixelFormat format);
@@ -671,7 +672,9 @@ to query availability of given format.
     @gl_extension{EXT,texture_rg} being present or not. If you wish to use @ref PixelFormat::Red and @ref PixelFormat::RG instead, specify the GL-specific
     pixel format directly instead of using the generic enum.
 
-@see @ref pixelType(), @ref compressedPixelFormat()
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
+@see @ref pixelType(), @ref compressedPixelFormat(),
+    @ref genericPixelFormat(PixelFormat, PixelType)
 */
 MAGNUM_GL_EXPORT PixelFormat pixelFormat(Magnum::PixelFormat format);
 
@@ -687,7 +690,10 @@ In case @ref isPixelFormatImplementationSpecific() returns @cpp false @ce for
 Not all generic pixel formats may be available on all targets and this function
 expects that given format is available on the target. Use @ref hasPixelFormat()
 to query availability of given format.
-@see @ref pixelFormat(), @ref compressedPixelFormat()
+
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
+@see @ref pixelFormat(), @ref compressedPixelFormat(),
+    @ref genericPixelFormat(PixelFormat, PixelType)
 */
 MAGNUM_GL_EXPORT PixelType pixelType(Magnum::PixelFormat format, UnsignedInt extra = 0);
 
@@ -708,6 +714,27 @@ CORRADE_DEPRECATED("use pixelFormatSize() instead") inline UnsignedInt pixelSize
 }
 #endif
 
+/**
+@brief Convert OpenGL pixel format and type combination to a generic pixel format
+@m_since_latest
+
+Returns @ref Containers::NullOpt if given combination doesn't match any generic
+pixel format. Otherwise the returned value will result in the same @p format
+and @p type when passed back to @ref pixelFormat(Magnum::PixelFormat) and
+@ref pixelType(Magnum::PixelFormat, UnsignedInt).
+
+An exception is sRGB formats --- those map to the same OpenGL format + type
+combination, e.g. @ref Magnum::PixelFormat::RGBA8Unorm and
+@relativeref{Magnum::PixelFormat,RGBA8Srgb} both result in
+@ref GL::PixelFormat::RGBA + @ref GL::PixelType::UnsignedByte. This function
+always maps the OpenGL format + type combination to the linear type, not sRGB.
+
+Unlike mapping *from* a generic pixel format, the inverse operation is done
+with an @f$ \mathcal{O}(n) @f$ complexity.
+@see @ref genericCompressedPixelFormat(CompressedPixelFormat)
+*/
+MAGNUM_GL_EXPORT Containers::Optional<Magnum::PixelFormat> genericPixelFormat(PixelFormat format, PixelType type);
+
 /** @debugoperatorenum{PixelFormat} */
 MAGNUM_GL_EXPORT Debug& operator<<(Debug& debug, PixelFormat value);
 
@@ -2103,6 +2130,7 @@ expected to be valid.
     extension. Such check is outside of the scope of this function and you are
     expected to verify extension availability before using such format.
 
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
 @see @ref compressedPixelFormat(), @ref hasPixelFormat(),
     @ref hasTextureFormat()
 */
@@ -2120,10 +2148,34 @@ returns @ref compressedPixelFormatUnwrap() cast to @ref GL::CompressedPixelForma
 Not all generic pixel formats may be available on all targets and this function
 expects that given format is available on the target. Use
 @ref hasCompressedPixelFormat() to query availability of given format.
-@see @ref pixelFormat(), @ref textureFormat()
+
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
+@see @ref pixelFormat(), @ref textureFormat(),
+    @ref genericCompressedPixelFormat(CompressedPixelFormat)
 */
 MAGNUM_GL_EXPORT CompressedPixelFormat compressedPixelFormat(Magnum::CompressedPixelFormat format);
 
+/**
+@brief Convert OpenGL compressed pixel format to a generic compressed pixel format
+@m_since_latest
+
+Returns @ref Containers::NullOpt if given format doesn't match any generic
+pixel format. Otherwise the returned value will result in the same @p format
+when passed back to @ref compressedPixelFormat(Magnum::CompressedPixelFormat).
+
+An exception is ASTC float and normalized formats --- those map to the same
+OpenGL format, e.g. @ref Magnum::CompressedPixelFormat::Astc4x4RGBAUnorm and
+@relativeref{Magnum::CompressedPixelFormat,Astc4x4RGBAF} both result in
+@ref GL::CompressedPixelFormat::RGBAAstc4x4. To avoid potential information
+loss, this function always maps the OpenGL ASTC format back to the float
+variant.
+
+Unlike mapping *from* a generic pixel format, the inverse operation is done
+with an @f$ \mathcal{O}(n) @f$ complexity.
+@see @ref genericPixelFormat(PixelFormat, PixelType)
+*/
+MAGNUM_GL_EXPORT Containers::Optional<Magnum::CompressedPixelFormat> genericCompressedPixelFormat(CompressedPixelFormat format);
+
 /** @debugoperatorenum{CompressedPixelFormat} */
 MAGNUM_GL_EXPORT Debug& operator<<(Debug& debug, CompressedPixelFormat value);
 
diff --git a/src/Magnum/GL/Test/PixelFormatTest.cpp b/src/Magnum/GL/Test/PixelFormatTest.cpp
index 2e4227346..d475026af 100644
--- a/src/Magnum/GL/Test/PixelFormatTest.cpp
+++ b/src/Magnum/GL/Test/PixelFormatTest.cpp
@@ -24,6 +24,7 @@
 */
 
 #include <sstream>
+#include <Corrade/Containers/Optional.h>
 #include <Corrade/TestSuite/Tester.h>
 #include <Corrade/Utility/DebugStl.h>
 
@@ -50,6 +51,7 @@ struct PixelFormatTest: TestSuite::Tester {
     void mapTextureFormatImplementationSpecific();
     void mapTextureFormatUnsupported();
     void mapTextureFormatInvalid();
+    void mapGenericFormatUnsupported();
 
     void size();
     void sizeInvalid();
@@ -61,6 +63,7 @@ struct PixelFormatTest: TestSuite::Tester {
     void mapCompressedTextureFormatImplementationSpecific();
     void mapCompressedTextureFormatUnsupported();
     void mapCompressedTextureFormatInvalid();
+    void mapGenericCompressedFormatUnsupported();
 
     void debugPixelFormat();
     void debugPixelType();
@@ -80,6 +83,7 @@ PixelFormatTest::PixelFormatTest() {
               &PixelFormatTest::mapTextureFormatImplementationSpecific,
               &PixelFormatTest::mapTextureFormatUnsupported,
               &PixelFormatTest::mapTextureFormatInvalid,
+              &PixelFormatTest::mapGenericFormatUnsupported,
 
               &PixelFormatTest::size,
               &PixelFormatTest::sizeInvalid,
@@ -91,6 +95,7 @@ PixelFormatTest::PixelFormatTest() {
               &PixelFormatTest::mapCompressedTextureFormatImplementationSpecific,
               &PixelFormatTest::mapCompressedTextureFormatUnsupported,
               &PixelFormatTest::mapCompressedTextureFormatInvalid,
+              &PixelFormatTest::mapGenericCompressedFormatUnsupported,
 
               &PixelFormatTest::debugPixelFormat,
               &PixelFormatTest::debugPixelType,
@@ -103,12 +108,18 @@ void PixelFormatTest::mapFormatTypeTextureFormat() {
     CORRADE_VERIFY(hasPixelFormat(Magnum::PixelFormat::RGBA8Unorm));
     CORRADE_COMPARE(pixelFormat(Magnum::PixelFormat::RGBA8Unorm), PixelFormat::RGBA);
     CORRADE_COMPARE(pixelType(Magnum::PixelFormat::RGBA8Unorm), PixelType::UnsignedByte);
+    CORRADE_COMPARE(genericPixelFormat(PixelFormat::RGB, PixelType::UnsignedByte), Magnum::PixelFormat::RGB8Unorm);
     #ifndef MAGNUM_TARGET_GLES2
     CORRADE_VERIFY(hasTextureFormat(Magnum::PixelFormat::RGBA8Unorm));
     CORRADE_COMPARE(textureFormat(Magnum::PixelFormat::RGBA8Unorm), TextureFormat::RGBA8);
+    CORRADE_COMPARE(genericPixelFormat(TextureFormat::RGB8), Magnum::PixelFormat::RGB8Unorm);
     #else
     CORRADE_VERIFY(!hasTextureFormat(Magnum::PixelFormat::RGBA8Unorm));
+    CORRADE_COMPARE(genericPixelFormat(TextureFormat::RGB), Containers::NullOpt);
     #endif
+    /* sRGB formats have N:1 mapping, conversion back is losing the sRGB bit */
+    CORRADE_COMPARE(genericPixelFormat(pixelFormat(Magnum::PixelFormat::R8Srgb), pixelType(Magnum::PixelFormat::R8Srgb)), Magnum::PixelFormat::R8Unorm);
+    CORRADE_COMPARE(genericPixelFormat(pixelFormat(Magnum::PixelFormat::RGBA8Srgb), pixelType(Magnum::PixelFormat::RGBA8Srgb)), Magnum::PixelFormat::RGBA8Unorm);
 
     /* This goes through the first 16 bits, which should be enough. Going
        through 32 bits takes 8 seconds, too much. */
@@ -134,11 +145,51 @@ void PixelFormatTest::mapFormatTypeTextureFormat() {
                     CORRADE_VERIFY(hasPixelFormat(Magnum::PixelFormat::format)); \
                     CORRADE_COMPARE(pixelFormat(Magnum::PixelFormat::format), Magnum::GL::PixelFormat::expectedFormat); \
                     CORRADE_COMPARE(pixelType(Magnum::PixelFormat::format), Magnum::GL::PixelType::expectedType); \
+                    CORRADE_COMPARE(genericPixelFormat(Magnum::GL::PixelFormat::expectedFormat, Magnum::GL::PixelType::expectedType), Magnum::PixelFormat::format); \
                     CORRADE_VERIFY(hasTextureFormat(Magnum::PixelFormat::format)); \
                     CORRADE_COMPARE(textureFormat(Magnum::PixelFormat::format), Magnum::GL::TextureFormat::expectedTextureFormat); \
+                    CORRADE_COMPARE(genericPixelFormat(Magnum::GL::TextureFormat::expectedTextureFormat), Magnum::PixelFormat::format); \
+                    ++nextHandled; \
+                    continue;
+            /* For duplicate format/type mappings compared to _c() it only
+               checks the forward mapping and genericPixelFormat() from a
+               TextureFormat. The duplicate mapping is tested in the touchstone
+               verification above. */
+            #define _d(format, expectedFormat, expectedType, expectedTextureFormat) \
+                case Magnum::PixelFormat::format: \
+                    CORRADE_COMPARE(nextHandled, i); \
+                    CORRADE_COMPARE(firstUnhandled, 0xffff); \
+                    CORRADE_VERIFY(hasPixelFormat(Magnum::PixelFormat::format)); \
+                    CORRADE_COMPARE(pixelFormat(Magnum::PixelFormat::format), Magnum::GL::PixelFormat::expectedFormat); \
+                    CORRADE_COMPARE(pixelType(Magnum::PixelFormat::format), Magnum::GL::PixelType::expectedType); \
+                    CORRADE_VERIFY(hasTextureFormat(Magnum::PixelFormat::format)); \
+                    CORRADE_COMPARE(textureFormat(Magnum::PixelFormat::format), Magnum::GL::TextureFormat::expectedTextureFormat); \
+                    CORRADE_COMPARE(genericPixelFormat(Magnum::GL::TextureFormat::expectedTextureFormat), Magnum::PixelFormat::format); \
                     ++nextHandled; \
                     continue;
             #define _n(format, expectedFormat, expectedType) \
+                case Magnum::PixelFormat::format: { \
+                    CORRADE_COMPARE(nextHandled, i); \
+                    CORRADE_COMPARE(firstUnhandled, 0xffff); \
+                    CORRADE_VERIFY(hasPixelFormat(Magnum::PixelFormat::format)); \
+                    CORRADE_COMPARE(pixelFormat(Magnum::PixelFormat::format), Magnum::GL::PixelFormat::expectedFormat); \
+                    CORRADE_COMPARE(pixelType(Magnum::PixelFormat::format), Magnum::GL::PixelType::expectedType); \
+                    CORRADE_COMPARE(genericPixelFormat(Magnum::GL::PixelFormat::expectedFormat, Magnum::GL::PixelType::expectedType), Magnum::PixelFormat::format); \
+                    CORRADE_VERIFY(!hasTextureFormat(Magnum::PixelFormat::format)); \
+                    std::ostringstream out; \
+                    { /* Redirected otherwise graceful assert would abort */ \
+                        Error redirectError{&out}; \
+                        textureFormat(Magnum::PixelFormat::format); \
+                    } \
+                    Debug{Debug::Flag::NoNewlineAtTheEnd} << out.str(); \
+                    ++nextHandled; \
+                    continue; \
+                }
+            /* For duplicate format/type mappings compared to _n() it only
+               checks the forward mapping and genericPixelFormat() from a
+               TextureFormat. The duplicate mapping is tested in the touchstone
+               verification above. */
+            #define _dn(format, expectedFormat, expectedType) \
                 case Magnum::PixelFormat::format: { \
                     CORRADE_COMPARE(nextHandled, i); \
                     CORRADE_COMPARE(firstUnhandled, 0xffff); \
@@ -175,6 +226,7 @@ void PixelFormatTest::mapFormatTypeTextureFormat() {
             #include "Magnum/GL/Implementation/pixelFormatMapping.hpp"
             #undef _s
             #undef _n
+            #undef _d
             #undef _c
         }
         #ifdef CORRADE_TARGET_GCC
@@ -319,6 +371,18 @@ void PixelFormatTest::mapTextureFormatInvalid() {
         "GL::textureFormat(): invalid format PixelFormat(0x123)\n");
 }
 
+void PixelFormatTest::mapGenericFormatUnsupported() {
+    /* These don't have any generic equivalent yet */
+    #ifndef MAGNUM_TARGET_WEBGL
+    CORRADE_COMPARE(genericPixelFormat(PixelFormat::BGRA, PixelType::UnsignedByte), Containers::NullOpt);
+    #endif
+    CORRADE_COMPARE(genericPixelFormat(PixelFormat::RGBA, PixelType::UnsignedShort565), Containers::NullOpt);
+    CORRADE_COMPARE(genericPixelFormat(TextureFormat::RGB565), Containers::NullOpt);
+    /* For compressed texture formats it returns NullOpt too, instead of
+       asserting. See comment in the source for reasons. */
+    CORRADE_COMPARE(genericPixelFormat(TextureFormat::CompressedR11Eac), Containers::NullOpt);
+}
+
 void PixelFormatTest::size() {
     #ifndef MAGNUM_TARGET_GLES
     CORRADE_COMPARE(pixelFormatSize(PixelFormat::RGB, PixelType::UnsignedByte332), 1);
@@ -350,6 +414,9 @@ void PixelFormatTest::mapCompressedFormatTextureFormat() {
     CORRADE_COMPARE(compressedPixelFormat(Magnum::CompressedPixelFormat::Bc1RGBAUnorm), CompressedPixelFormat::RGBAS3tcDxt1);
     CORRADE_VERIFY(hasTextureFormat(Magnum::CompressedPixelFormat::Astc8x8RGBASrgb));
     CORRADE_COMPARE(textureFormat(Magnum::CompressedPixelFormat::Astc8x8RGBASrgb), TextureFormat::CompressedSRGB8Alpha8Astc8x8);
+    /* ASTC Unorm formats have N:1 mapping, conversion back is losing the
+       Unorm/F distinction */
+    CORRADE_COMPARE(genericCompressedPixelFormat(compressedPixelFormat(Magnum::CompressedPixelFormat::Astc4x4RGBAUnorm)), Magnum::CompressedPixelFormat::Astc4x4RGBAF);
 
     /* This goes through the first 16 bits, which should be enough. Going
        through 32 bits takes 8 seconds, too much. */
@@ -369,6 +436,21 @@ void PixelFormatTest::mapCompressedFormatTextureFormat() {
         #endif
         switch(format) {
             #define _c(format, expectedFormat) \
+                case Magnum::CompressedPixelFormat::format: \
+                    CORRADE_COMPARE(nextHandled, i); \
+                    CORRADE_COMPARE(firstUnhandled, 0xffff); \
+                    CORRADE_VERIFY(hasCompressedPixelFormat(Magnum::CompressedPixelFormat::format)); \
+                    CORRADE_COMPARE(genericCompressedPixelFormat(Magnum::GL::CompressedPixelFormat::expectedFormat), Magnum::CompressedPixelFormat::format); \
+                    CORRADE_VERIFY(hasTextureFormat(Magnum::CompressedPixelFormat::format)); \
+                    CORRADE_COMPARE(compressedPixelFormat(Magnum::CompressedPixelFormat::format), Magnum::GL::CompressedPixelFormat::expectedFormat); \
+                    CORRADE_COMPARE(textureFormat(Magnum::CompressedPixelFormat::format), Magnum::GL::TextureFormat::Compressed ## expectedFormat); \
+                    CORRADE_COMPARE(genericCompressedPixelFormat(Magnum::GL::TextureFormat::Compressed ## expectedFormat), Magnum::CompressedPixelFormat::format); \
+                    ++nextHandled; \
+                    continue;
+            /* For duplicate mappings compared to _c() it only checks the
+               forward mapping. The duplicate mapping is tested in the
+               touchstone verification above */
+            #define _d(format, expectedFormat) \
                 case Magnum::CompressedPixelFormat::format: \
                     CORRADE_COMPARE(nextHandled, i); \
                     CORRADE_COMPARE(firstUnhandled, 0xffff); \
@@ -396,6 +478,7 @@ void PixelFormatTest::mapCompressedFormatTextureFormat() {
                 }
             #include "Magnum/GL/Implementation/compressedPixelFormatMapping.hpp"
             #undef _s
+            #undef _d
             #undef _c
         }
         #ifdef CORRADE_TARGET_GCC
@@ -501,6 +584,17 @@ void PixelFormatTest::mapCompressedTextureFormatInvalid() {
         "GL::textureFormat(): invalid format CompressedPixelFormat(0x123)\n");
 }
 
+void PixelFormatTest::mapGenericCompressedFormatUnsupported() {
+    /* Generic formats don't have any generic equivalent yet (heh) */
+    #ifndef MAGNUM_TARGET_GLES
+    CORRADE_COMPARE(genericCompressedPixelFormat(CompressedPixelFormat::Red), Containers::NullOpt);
+    CORRADE_COMPARE(genericCompressedPixelFormat(TextureFormat::CompressedRed), Containers::NullOpt);
+    #endif
+    /* For uncompressed texture formats it returns NullOpt too, instead of
+       asserting. See comment in the source for reasons. */
+    CORRADE_COMPARE(genericCompressedPixelFormat(TextureFormat::RGB), Containers::NullOpt);
+}
+
 void PixelFormatTest::debugPixelFormat() {
     std::ostringstream out;
 
diff --git a/src/Magnum/GL/TextureFormat.cpp b/src/Magnum/GL/TextureFormat.cpp
index 744f7c50f..c436070bf 100644
--- a/src/Magnum/GL/TextureFormat.cpp
+++ b/src/Magnum/GL/TextureFormat.cpp
@@ -34,9 +34,11 @@
 
 namespace Magnum { namespace GL {
 
-/* the textureFormat() and hasTextureFormat() utilities share mapping tables
-   with pixelFormat() / hasPixelFormat() so are defined in PixelFormat.cpp
-   instead (and tested there too) */
+/* compressed textureFormat(), hasTextureFormat() and
+   genericCompressedPixelFormat(TextureFormat) utilities share mapping tables
+   with compressedPixelFormat(), hasCompressedPixelFormat() and
+   genericCompressedPixelFormat(CompressedPixelFormat) so are defined in
+   PixelFormat.cpp instead (and tested there too) */
 
 #ifndef DOXYGEN_GENERATING_OUTPUT
 Debug& operator<<(Debug& debug, const TextureFormat value) {
diff --git a/src/Magnum/GL/TextureFormat.h b/src/Magnum/GL/TextureFormat.h
index 533bd8a59..424245c17 100644
--- a/src/Magnum/GL/TextureFormat.h
+++ b/src/Magnum/GL/TextureFormat.h
@@ -2625,6 +2625,7 @@ and other format-specific extensions are supported.
     extension. Such check is outside of the scope of this function and you are
     expected to verify extension availability before using such format.
 
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
 @see @ref textureFormat(), @ref hasPixelFormat(),
     @ref hasCompressedPixelFormat()
 */
@@ -2647,7 +2648,9 @@ manually based on whether @ref Texture::setImage() or
 @ref Texture::setStorage() is used and whether @gl_extension{EXT,texture_storage}
 and other format-specific extensions are supported.
 
-@see @ref pixelType(), @ref compressedPixelFormat()
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
+@see @ref pixelType(), @ref compressedPixelFormat(),
+    @ref genericPixelFormat(TextureFormat)
 */
 MAGNUM_GL_EXPORT TextureFormat textureFormat(Magnum::PixelFormat format);
 
@@ -2669,6 +2672,7 @@ performed.
     extension. Such check is outside of the scope of this function and you are
     expected to verify extension availability before using such format.
 
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
 @see @ref textureFormat(), @ref hasCompressedPixelFormat(),
     @ref hasPixelFormat()
 */
@@ -2688,12 +2692,51 @@ an implementation-specific pixel format to an OpenGL texture format can't be
 performed.
 
 Not all generic pixel formats may be available on all targets and this function
-expects that given format is available on the target. Use @ref hasTextureFormat()
-to query availability of given format.
-@see @ref compressedPixelFormat(), @ref pixelFormat()
+expects that given format is available on the target. Use
+@ref hasTextureFormat() to query availability of given format.
+
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
+@see @ref compressedPixelFormat(), @ref pixelFormat(),
+    @ref genericCompressedPixelFormat(TextureFormat)
 */
 MAGNUM_GL_EXPORT TextureFormat textureFormat(Magnum::CompressedPixelFormat format);
 
+/**
+@brief Convert OpenGL texture format to a generic pixel format
+@m_since_latest
+
+Returns @ref Containers::NullOpt if given format is compressed or if it doesn't
+match any generic pixel format. Otherwise the returned value will result in the
+same @p format when passed back to @ref textureFormat(Magnum::PixelFormat).
+
+Unlike mapping *from* a generic pixel format, the inverse operation is done
+with an @f$ \mathcal{O}(n) @f$ complexity.
+@see @ref genericCompressedPixelFormat(TextureFormat)
+*/
+MAGNUM_GL_EXPORT Containers::Optional<Magnum::PixelFormat> genericPixelFormat(TextureFormat format);
+
+/**
+@brief Convert OpenGL compressed texture format to a generic compressed pixel format
+@m_since_latest
+
+Returns @ref Containers::NullOpt if given format is not compressed or if it
+doesn't match any generic compressed pixel format. Otherwise the returned value
+will result in the same @p format when passed back to
+@ref textureFormat(Magnum::CompressedPixelFormat).
+
+An exception is ASTC float and normalized formats --- those map to the same
+OpenGL format, e.g. @ref Magnum::CompressedPixelFormat::Astc4x4RGBAUnorm and
+@relativeref{Magnum::CompressedPixelFormat,Astc4x4RGBAF} both result in
+@ref GL::TextureFormat::CompressedRGBAAstc4x4. To avoid potential information
+loss, this function always maps the OpenGL ASTC format back to the float
+variant.
+
+Unlike mapping *from* a generic pixel format, the inverse operation is done
+with an @f$ \mathcal{O}(n) @f$ complexity.
+@see @ref genericPixelFormat(TextureFormat)
+*/
+MAGNUM_GL_EXPORT Containers::Optional<Magnum::CompressedPixelFormat> genericCompressedPixelFormat(TextureFormat format);
+
 /**
 @debugoperatorenum{TextureFormat}
 @m_since{2019,10}
diff --git a/src/Magnum/PixelFormat.h b/src/Magnum/PixelFormat.h
index 759bf66cc..c1ccb1348 100644
--- a/src/Magnum/PixelFormat.h
+++ b/src/Magnum/PixelFormat.h
@@ -48,17 +48,20 @@ Can act also as a wrapper for implementation-specific pixel format values using
 generic and implementation-specific formats can be done using
 @ref isPixelFormatImplementationSpecific().
 
-In case of OpenGL, corresponds to @ref GL::PixelFormat and @ref GL::PixelType
-and is convertible to them using @ref GL::pixelFormat() and
-@ref GL::pixelType(). See documentation of each value for more information
-about the mapping. Note that not every format is available on all targets, use
-@ref GL::hasPixelFormat() to check for its presence.
-
-In case of Vulkan, corresponds to @ref Vk::PixelFormat and is convertible
-to it using @ref Vk::pixelFormat(Magnum::PixelFormat). See documentation of
-each value for more information about the mapping. Note that not every format
-may be available, use @ref Vk::hasPixelFormat(Magnum::PixelFormat) to check for
-its presence.
+In case of OpenGL, corresponds to @ref GL::PixelFormat, @ref GL::PixelType
+and uncompressed @ref GL::TextureFormat values, is convertible to them using
+@ref GL::pixelFormat(), @ref GL::pixelType() and @ref GL::textureFormat(), and
+an inverse mapping can be done via @ref GL::genericPixelFormat(PixelFormat, PixelType)
+and @ref GL::genericPixelFormat(TextureFormat). See documentation of each value
+for more information about the mapping. Note that not every format is available
+on all targets, use @ref GL::hasPixelFormat() to check for its presence.
+
+In case of Vulkan, corresponds to uncompressed @ref Vk::PixelFormat values, is
+convertible to it using @ref Vk::pixelFormat(Magnum::PixelFormat), and an
+inverse mapping can be done via @ref Vk::genericPixelFormat(). See
+documentation of each value for more information about the mapping. Note that
+not every format may be available, use
+@ref Vk::hasPixelFormat(Magnum::PixelFormat) to check for its presence.
 
 For D3D, corresponds to @m_class{m-doc-external} [DXGI_FORMAT](https://docs.microsoft.com/en-us/windows/win32/api/dxgiformat/ne-dxgiformat-dxgi_format)
 and import is provided by the @ref Trade::DdsImporter "DdsImporter" plugin; for
@@ -982,17 +985,22 @@ Can act also as a wrapper for implementation-specific pixel format values using
 Distinction between generic and implementation-specific formats can be done
 using @ref isCompressedPixelFormatImplementationSpecific().
 
-In case of OpenGL, corresponds to @ref GL::CompressedPixelFormat and is
-convertible to it using @ref GL::compressedPixelFormat(). See documentation of
+In case of OpenGL, corresponds to @ref GL::CompressedPixelFormat and compressed
+@ref GL::TextureFormat values, is convertible to them using
+@ref GL::compressedPixelFormat() and @ref GL::textureFormat(), and an inverse
+mapping can be done via @ref GL::genericCompressedPixelFormat(CompressedPixelFormat)
+and @ref GL::genericCompressedPixelFormat(TextureFormat). See documentation of
 each value for more information about the mapping. Note that not every format
 is available on all targets, use @ref GL::hasCompressedPixelFormat() to check
 for its presence.
 
-In case of Vulkan, corresponds to @ref Vk::PixelFormat and is convertible to it
-using @ref Vk::pixelFormat(Magnum::CompressedPixelFormat). See documentation
-of each value for more information about the mapping. Note that not every
-format may be available, use @ref Vk::hasPixelFormat(Magnum::CompressedPixelFormat)
-to check for its presence.
+In case of Vulkan, corresponds to compressed @ref Vk::PixelFormat values, is
+convertible to it using @ref Vk::pixelFormat(Magnum::CompressedPixelFormat),
+and an inverse mapping can be done via @ref Vk::genericCompressedPixelFormat().
+See documentation of each value for more information about the mapping. Note
+that not every format may be available, use
+@ref Vk::hasPixelFormat(Magnum::CompressedPixelFormat) to check for its
+presence.
 
 For D3D, corresponds to @m_class{m-doc-external} [DXGI_FORMAT](https://docs.microsoft.com/en-us/windows/win32/api/dxgiformat/ne-dxgiformat-dxgi_format)
 and import is provided by the @ref Trade::DdsImporter "DdsImporter" plugin; for
diff --git a/src/Magnum/Vk/Implementation/compressedPixelFormatMapping.hpp b/src/Magnum/Vk/Implementation/compressedPixelFormatMapping.hpp
index 2ce7830e6..e7dfc4f7f 100644
--- a/src/Magnum/Vk/Implementation/compressedPixelFormatMapping.hpp
+++ b/src/Magnum/Vk/Implementation/compressedPixelFormatMapping.hpp
@@ -23,7 +23,11 @@
     DEALINGS IN THE SOFTWARE.
 */
 
-/* See Magnum/Vk/Enums.cpp and Magnum/Vk/Test/EnumsTest.cpp */
+/* See Magnum/Vk/Enums.cpp and Magnum/Vk/Test/EnumsTest.cpp. _c() is a mapping,
+   _s() denotes a skipped value (so the enum numbering is preserved), _d()
+   denotes a _c() value with duplicated result, i.e. a N:1 mapping from a
+   generic format. The _c2() is just a shortand for the input and output name
+   being the same. */
 #ifdef _c
 #define _c2(input) _c(input, input)
 _c2(Bc1RGBUnorm)
@@ -128,12 +132,12 @@ _s(Astc6x6x6RGBASrgb) //, ASTC_6x6x6_SRGB_BLOCK)
 _s(Astc6x6x6RGBAF) //, ASTC_6x6x6_SFLOAT_BLOCK_EXT)
 
 /* https://github.com/KhronosGroup/Vulkan-Docs/issues/512 */
-_c(PvrtcRGB2bppUnorm, PvrtcRGBA2bppUnorm)
-_c(PvrtcRGB2bppSrgb, PvrtcRGBA2bppSrgb)
+_d(PvrtcRGB2bppUnorm, PvrtcRGBA2bppUnorm)
+_d(PvrtcRGB2bppSrgb, PvrtcRGBA2bppSrgb)
 _c2(PvrtcRGBA2bppUnorm)
 _c2(PvrtcRGBA2bppSrgb)
-_c(PvrtcRGB4bppUnorm, PvrtcRGBA4bppUnorm)
-_c(PvrtcRGB4bppSrgb, PvrtcRGBA4bppSrgb)
+_d(PvrtcRGB4bppUnorm, PvrtcRGBA4bppUnorm)
+_d(PvrtcRGB4bppSrgb, PvrtcRGBA4bppSrgb)
 _c2(PvrtcRGBA4bppUnorm)
 _c2(PvrtcRGBA4bppSrgb)
 #undef _c2
diff --git a/src/Magnum/Vk/PixelFormat.cpp b/src/Magnum/Vk/PixelFormat.cpp
index b50d83413..9d01b0a8a 100644
--- a/src/Magnum/Vk/PixelFormat.cpp
+++ b/src/Magnum/Vk/PixelFormat.cpp
@@ -26,6 +26,7 @@
 #include "PixelFormat.h"
 
 #include <Corrade/Containers/ArrayView.h>
+#include <Corrade/Containers/Optional.h>
 #include <Corrade/Utility/Debug.h>
 
 #include "Magnum/PixelFormat.h"
@@ -46,9 +47,11 @@ constexpr PixelFormat PixelFormatMapping[] {
 constexpr PixelFormat CompressedPixelFormatMapping[] {
     /* GCC 4.8 doesn't like just a {} for default enum values */
     #define _c(input, format) PixelFormat::Compressed ## format,
+    #define _d _c
     #define _s(input) PixelFormat{},
     #include "Magnum/Vk/Implementation/compressedPixelFormatMapping.hpp"
     #undef _s
+    #undef _d
     #undef _c
 };
 
@@ -245,4 +248,50 @@ PixelFormat pixelFormat(const Magnum::CompressedPixelFormat format) {
     return out;
 }
 
+Containers::Optional<Magnum::PixelFormat> genericPixelFormat(const PixelFormat format) {
+    switch(format) {
+        #define _c(format)                                                  \
+            case PixelFormat::format:                                       \
+                return Magnum::PixelFormat::format;
+        #include "Magnum/Vk/Implementation/pixelFormatMapping.hpp"
+        #undef _c
+
+        /* For compressed formats it returns NullOpt too instead of asserting,
+           as -- compared to the generic-to-Vk translation, which is O(1) --
+           the inverse mapping is potentially a linear lookup and forcing the
+           user to check some isPixelFormatCompressed() first (which would do
+           another linear lookup) makes no sense from a perf PoV. Plus for
+           unknown formats it's unknown whether it's a compressed format or
+           not, and the function suddenly starting to assert when a format
+           becomes known isn't good for backwards compatibility. */
+        default:
+            return {};
+    }
+}
+
+Containers::Optional<Magnum::CompressedPixelFormat> genericCompressedPixelFormat(const PixelFormat format) {
+    switch(format) {
+        #define _c(input, format)                                           \
+            case PixelFormat::Compressed ## format:                         \
+                return Magnum::CompressedPixelFormat::input;
+        #define _d(input, format)
+        #define _s(input)
+        #include "Magnum/Vk/Implementation/compressedPixelFormatMapping.hpp"
+        #undef _s
+        #undef _d
+        #undef _c
+
+       /* For uncompressed formats it returns NullOpt too instead of asserting,
+          as -- compared to the generic-to-GL translation, which is O(1) -- the
+          inverse mapping is potentially a linear lookup and forcing the user
+          to check some isTextureFormatCompressed() first (which would do
+          another linear lookup) makes no sense from a perf PoV. Plus for
+          unknown formats it's unknown whether it's a compressed format or not,
+          and the function suddenly starting to assert when a format becomes
+          known isn't good for backwards compatibility. */
+        default:
+            return {};
+    }
+}
+
 }}
diff --git a/src/Magnum/Vk/PixelFormat.h b/src/Magnum/Vk/PixelFormat.h
index 971061c05..4912e5b10 100644
--- a/src/Magnum/Vk/PixelFormat.h
+++ b/src/Magnum/Vk/PixelFormat.h
@@ -30,7 +30,7 @@
 #include "Magnum/Vk/visibility.h"
 
 /** @file
- * @brief Enum @ref Magnum::Vk::PixelFormat, function @ref Magnum::Vk::hasPixelFormat(), @ref Magnum::Vk::pixelFormat()
+ * @brief Enum @ref Magnum::Vk::PixelFormat, function @ref Magnum::Vk::hasPixelFormat(), @ref Magnum::Vk::pixelFormat(), @ref Magnum::Vk::genericPixelFormat(), @ref Magnum::Vk::genericCompressedPixelFormat()
  * @m_since_latest
  */
 
@@ -1413,6 +1413,7 @@ be valid.
     extension. Such check is outside of the scope of this function and you are
     expected to verify extension availability before using such format.
 
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
 @see @ref pixelFormat(Magnum::PixelFormat)
 */
 MAGNUM_VK_EXPORT bool hasPixelFormat(Magnum::PixelFormat format);
@@ -1430,6 +1431,7 @@ expected to be valid.
     extension. Such check is outside of the scope of this function and you are
     expected to verify extension availability before using such format.
 
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
 @see @ref pixelFormat(Magnum::CompressedPixelFormat)
 */
 MAGNUM_VK_EXPORT bool hasPixelFormat(Magnum::CompressedPixelFormat format);
@@ -1447,6 +1449,9 @@ cast to @ref PixelFormat.
 Not all generic pixel formats have a Vulkan equivalent and this function
 expects that given format is available. Use
 @ref hasPixelFormat(Magnum::PixelFormat) to query availability of given format.
+
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
+@see @ref genericPixelFormat(PixelFormat)
 */
 MAGNUM_VK_EXPORT PixelFormat pixelFormat(Magnum::PixelFormat format);
 
@@ -1462,11 +1467,50 @@ assumes @p format stores a Vulkan-specific format and returns
 
 Not all generic pixel formats have a Vulkan equivalent and this function
 expects that given format is available. Use
-@ref hasPixelFormat(Magnum::CompressedPixelFormat) to query availability of given
-format.
+@ref hasPixelFormat(Magnum::CompressedPixelFormat) to query availability of
+given format.
+
+The mapping operation is done with an @f$ \mathcal{O}(1) @f$ complexity.
+@see @ref genericCompressedPixelFormat(PixelFormat)
 */
 MAGNUM_VK_EXPORT PixelFormat pixelFormat(Magnum::CompressedPixelFormat format);
 
+/**
+@brief Convert Vulkan pixel format to a generic pixel format
+@m_since_latest
+
+Returns @ref Containers::NullOpt if given format is compressed or if it doesn't
+match any generic pixel format. Otherwise the returned value will result in the
+same @p format when passed back to @ref pixelFormat(Magnum::PixelFormat).
+
+Unlike mapping *from* a generic pixel format, the inverse operation is done
+with an @f$ \mathcal{O}(n) @f$ complexity.
+@see @ref genericCompressedPixelFormat(PixelFormat)
+*/
+MAGNUM_VK_EXPORT Containers::Optional<Magnum::PixelFormat> genericPixelFormat(PixelFormat format);
+
+/**
+@brief Convert Vulkan compressed pixel format to a generic compressed pixel format
+@m_since_latest
+
+Returns @ref Containers::NullOpt if given format is not compressed or if it
+doesn't match any generic compressed pixel format. Otherwise the returned value
+will result in the same @p format when passed back to
+@ref pixelFormat(Magnum::CompressedPixelFormat).
+
+An exception is PVRTC formats --- the RGB and RGBA variants map to the same
+Vulkan format, e.g. @ref Magnum::CompressedPixelFormat::PvrtcRGB2bppSrgb and
+@relativeref{Magnum::CompressedPixelFormat,PvrtcRGBA2bppSrgb} both result in
+@ref Vk::PixelFormat::CompressedPvrtcRGBA2bppSrgb. To avoid potential
+information loss, this function always maps the Vulkan PVRTC formats back to
+the RGBA variants.
+
+Unlike mapping *from* a generic pixel format, the inverse operation is done
+with an @f$ \mathcal{O}(n) @f$ complexity.
+@see @ref genericPixelFormat(PixelFormat)
+*/
+MAGNUM_VK_EXPORT Containers::Optional<Magnum::CompressedPixelFormat> genericCompressedPixelFormat(PixelFormat format);
+
 }}
 
 #endif
diff --git a/src/Magnum/Vk/Test/PixelFormatTest.cpp b/src/Magnum/Vk/Test/PixelFormatTest.cpp
index 0c9e5b798..280d62718 100644
--- a/src/Magnum/Vk/Test/PixelFormatTest.cpp
+++ b/src/Magnum/Vk/Test/PixelFormatTest.cpp
@@ -24,6 +24,7 @@
 */
 
 #include <sstream>
+#include <Corrade/Containers/Optional.h>
 #include <Corrade/TestSuite/Tester.h>
 #include <Corrade/Utility/DebugStl.h>
 
@@ -39,11 +40,13 @@ struct PixelFormatTest: TestSuite::Tester {
     void mapImplementationSpecific();
     void mapUnsupported();
     void mapInvalid();
+    void mapGenericUnsupported();
 
     void mapCompressed();
     void mapCompressedImplementationSpecific();
     void mapCompressedUnsupported();
     void mapCompressedInvalid();
+    void mapGenericCompressedUnsupported();
 
     void debug();
 };
@@ -53,11 +56,13 @@ PixelFormatTest::PixelFormatTest() {
               &PixelFormatTest::mapImplementationSpecific,
               &PixelFormatTest::mapUnsupported,
               &PixelFormatTest::mapInvalid,
+              &PixelFormatTest::mapGenericUnsupported,
 
               &PixelFormatTest::mapCompressed,
               &PixelFormatTest::mapCompressedImplementationSpecific,
               &PixelFormatTest::mapCompressedUnsupported,
               &PixelFormatTest::mapCompressedInvalid,
+              &PixelFormatTest::mapGenericCompressedUnsupported,
 
               &PixelFormatTest::debug});
 }
@@ -90,6 +95,7 @@ void PixelFormatTest::map() {
                     CORRADE_COMPARE(nextHandled, i); \
                     CORRADE_COMPARE(firstUnhandled, 0xffff); \
                     CORRADE_VERIFY(hasPixelFormat(Magnum::PixelFormat::format)); \
+                    CORRADE_COMPARE(genericPixelFormat(PixelFormat::format), Magnum::PixelFormat::format); \
                     CORRADE_COMPARE(pixelFormat(Magnum::PixelFormat::format), PixelFormat::format); \
                     { \
                         std::ostringstream out; \
@@ -166,11 +172,23 @@ void PixelFormatTest::mapInvalid() {
         "Vk::pixelFormat(): invalid format PixelFormat(0x123)\n");
 }
 
+void PixelFormatTest::mapGenericUnsupported() {
+    /* This one doesn't have any generic equivalent yet, and isn't in the
+       enum either */
+    CORRADE_COMPARE(genericPixelFormat(PixelFormat(VK_FORMAT_R5G6B5_UNORM_PACK16)), Containers::NullOpt);
+    /* For compressed texture formats it returns NullOpt too, instead of
+       asserting. See comment in the source for reasons. */
+    CORRADE_COMPARE(genericPixelFormat(PixelFormat::CompressedAstc4x4RGBAF), Containers::NullOpt);
+}
+
 void PixelFormatTest::mapCompressed() {
     /* Touchstone verification. Using Vulkan enums directly to sidestep
        potential problems in enum mapping as well. */
     CORRADE_VERIFY(hasPixelFormat(Magnum::CompressedPixelFormat::Bc1RGBAUnorm));
     CORRADE_COMPARE(pixelFormat(Magnum::CompressedPixelFormat::Bc1RGBAUnorm), PixelFormat(VK_FORMAT_BC1_RGBA_UNORM_BLOCK));
+    /* PVRTC RGB and RGBA formats have N:1 mapping, conversion back makes them
+       always RGBA */
+    CORRADE_COMPARE(genericCompressedPixelFormat(pixelFormat(Magnum::CompressedPixelFormat::PvrtcRGB4bppSrgb)), Magnum::CompressedPixelFormat::PvrtcRGBA4bppSrgb);
 
     /* This goes through the first 16 bits, which should be enough. Going
        through 32 bits takes 8 seconds, too much. */
@@ -190,6 +208,23 @@ void PixelFormatTest::mapCompressed() {
         #endif
         switch(format) {
             #define _c(format, expectedFormat) \
+                case Magnum::CompressedPixelFormat::format: \
+                    CORRADE_COMPARE(nextHandled, i); \
+                    CORRADE_COMPARE(firstUnhandled, 0xffff); \
+                    CORRADE_VERIFY(hasPixelFormat(Magnum::CompressedPixelFormat::format)); \
+                    CORRADE_COMPARE(genericCompressedPixelFormat(PixelFormat::Compressed ## expectedFormat), Magnum::CompressedPixelFormat::format); \
+                    CORRADE_COMPARE(pixelFormat(Magnum::CompressedPixelFormat::format), PixelFormat::Compressed ## expectedFormat); \
+                    { \
+                        std::ostringstream out; \
+                        Debug{&out} << pixelFormat(Magnum::CompressedPixelFormat::format); \
+                        CORRADE_COMPARE(out.str(), "Vk::PixelFormat::Compressed" #expectedFormat "\n"); \
+                    } \
+                    ++nextHandled; \
+                    continue;
+            /* For duplicate mappings compared to _c() it only checks the
+               forward mapping. The duplicate mapping is tested in the
+               touchstone verification above */
+            #define _d(format, expectedFormat) \
                 case Magnum::CompressedPixelFormat::format: \
                     CORRADE_COMPARE(nextHandled, i); \
                     CORRADE_COMPARE(firstUnhandled, 0xffff); \
@@ -267,6 +302,14 @@ void PixelFormatTest::mapCompressedInvalid() {
         "Vk::pixelFormat(): invalid format CompressedPixelFormat(0x123)\n");
 }
 
+void PixelFormatTest::mapGenericCompressedUnsupported() {
+    /* PVRTC2 doesn't have any generic equivalent yet */
+    CORRADE_COMPARE(genericPixelFormat(PixelFormat::CompressedPvrtc2RGBA2bppUnorm), Containers::NullOpt);
+    /* For uncompressed texture formats it returns NullOpt too, instead of
+       asserting. See comment in the source for reasons. */
+    CORRADE_COMPARE(genericCompressedPixelFormat(PixelFormat::RGB8Unorm), Containers::NullOpt);
+}
+
 void PixelFormatTest::debug() {
     std::ostringstream out;
     Debug{&out} << PixelFormat::RGB16UI << PixelFormat(-10007655);