diff --git a/doc/changelog.dox b/doc/changelog.dox
index 2c7aa5a5a..7c942f586 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -50,6 +50,11 @@ See also:
     @ref Color3us, @ref Color4us convenience typedefs for half-float, 8- and
     16-bit integer vector and color types
 -   New @ref VertexFormat enum for vertex formats and related utilities
+-   New @ref MeshPrimitive::Instances, @ref MeshPrimitive::Faces and
+    @ref MeshPrimitive::Edges primitive types for describing per-instance,
+    per-face and per-edge data. Those don't map to any common GPU API, but can
+    be used by various importers to provide access to mesh data that is not
+    necessarily GPU-friendly.
 
 @subsubsection changelog-latest-new-audio Audio library
 
diff --git a/src/Magnum/GL/Mesh.cpp b/src/Magnum/GL/Mesh.cpp
index 80980bd5e..d26778434 100644
--- a/src/Magnum/GL/Mesh.cpp
+++ b/src/Magnum/GL/Mesh.cpp
@@ -54,7 +54,10 @@ constexpr MeshPrimitive PrimitiveMapping[]{
     MeshPrimitive::LineStrip,
     MeshPrimitive::Triangles,
     MeshPrimitive::TriangleStrip,
-    MeshPrimitive::TriangleFan
+    MeshPrimitive::TriangleFan,
+    MeshPrimitive(~UnsignedInt{}), /* Instances */
+    MeshPrimitive(~UnsignedInt{}), /* Faces */
+    MeshPrimitive(~UnsignedInt{})  /* Edges */
 };
 
 constexpr MeshIndexType IndexTypeMapping[]{
diff --git a/src/Magnum/GL/Test/MeshTest.cpp b/src/Magnum/GL/Test/MeshTest.cpp
index 2cbe8422d..9569b6fcb 100644
--- a/src/Magnum/GL/Test/MeshTest.cpp
+++ b/src/Magnum/GL/Test/MeshTest.cpp
@@ -191,7 +191,10 @@ void MeshTest::mapPrimitiveImplementationSpecific() {
 }
 
 void MeshTest::mapPrimitiveUnsupported() {
-    CORRADE_SKIP("All primitive types are supported.");
+    std::ostringstream out;
+    Error redirectError{&out};
+    meshPrimitive(Magnum::MeshPrimitive::Instances);
+    CORRADE_COMPARE(out.str(), "GL::meshPrimitive(): unsupported primitive MeshPrimitive::Instances\n");
 }
 
 void MeshTest::mapPrimitiveInvalid() {
diff --git a/src/Magnum/Implementation/meshPrimitiveMapping.hpp b/src/Magnum/Implementation/meshPrimitiveMapping.hpp
index 0f503c8a4..5275a0ead 100644
--- a/src/Magnum/Implementation/meshPrimitiveMapping.hpp
+++ b/src/Magnum/Implementation/meshPrimitiveMapping.hpp
@@ -32,4 +32,7 @@ _c(LineStrip)
 _c(Triangles)
 _c(TriangleStrip)
 _c(TriangleFan)
+_c(Instances)
+_c(Faces)
+_c(Edges)
 #endif
diff --git a/src/Magnum/Mesh.h b/src/Magnum/Mesh.h
index 791ba69d6..4e8016572 100644
--- a/src/Magnum/Mesh.h
+++ b/src/Magnum/Mesh.h
@@ -135,7 +135,48 @@ enum class MeshPrimitive: UnsignedInt {
      * @def_vk_keyword{PRIMITIVE_TOPOLOGY_TRIANGLE_FAN,PrimitiveTopology}. Not
      * supported on D3D or Metal.
      */
-    TriangleFan
+    TriangleFan,
+
+    /**
+     * Per-instance data.
+     * @m_since_latest
+     *
+     * Has no direct mapping to GPU APIs, but can be used to annotate
+     * @ref Trade::MeshData containing per-instance data (such as colors,
+     * transformations or texture layers) and then used to populate an instance
+     * buffer. Index buffer has no defined meaning for instance data.
+     */
+    Instances,
+
+    /**
+     * Per-face data.
+     * @m_since_latest
+     *
+     * Can be used to annotate @ref Trade::MeshData containing data that are
+     * per-face, as opposed to per-vertex. Has no direct mapping to common GPU
+     * APIs, there it either has to be converted to per-vertex (which usually
+     * involves slightly duplicating the original per-vertex data) or accessed
+     * via a direct buffer/texture fetch from a shader using e.g.
+     * @glsl gl_VertexID @ce. Index buffer can be used to deduplicate per-face
+     * data.
+     */
+    Faces,
+
+    /**
+     * Per-edge data.
+     * @m_since_latest
+     *
+     * Can be used to annotate @ref Trade::MeshData containing data that are
+     * per-edge, as opposed to per-vertex. This is different from
+     * @ref MeshPrimitive::Lines as it has just one entry per line segment,
+     * instead of two. Has no direct mapping to common GPU APIs, there it has
+     * to be converted to per-vertex (which usually involves slightly
+     * duplicating the original per-vertex data). Index buffer can be used to
+     * deduplicate per-face data. Can also be used for example to describe a
+     * half-edge mesh representation.
+     * @see @ref Trade::meshAttributeCustom()
+     */
+    Edges
 };
 
 /** @debugoperatorenum{MeshPrimitive} */
diff --git a/src/Magnum/Vk/Enums.cpp b/src/Magnum/Vk/Enums.cpp
index cacdb8953..edfdff101 100644
--- a/src/Magnum/Vk/Enums.cpp
+++ b/src/Magnum/Vk/Enums.cpp
@@ -43,7 +43,10 @@ constexpr VkPrimitiveTopology PrimitiveTopologyMapping[]{
     VK_PRIMITIVE_TOPOLOGY_LINE_STRIP,
     VK_PRIMITIVE_TOPOLOGY_TRIANGLE_LIST,
     VK_PRIMITIVE_TOPOLOGY_TRIANGLE_STRIP,
-    VK_PRIMITIVE_TOPOLOGY_TRIANGLE_FAN
+    VK_PRIMITIVE_TOPOLOGY_TRIANGLE_FAN,
+    VkPrimitiveTopology(~UnsignedInt{}), /* Instances */
+    VkPrimitiveTopology(~UnsignedInt{}), /* Faces */
+    VkPrimitiveTopology(~UnsignedInt{})  /* Edges */
 };
 
 constexpr VkIndexType IndexTypeMapping[]{