diff --git a/src/Magnum/Trade/AbstractMaterialData.cpp b/src/Magnum/Trade/AbstractMaterialData.cpp
index aeec37042..0a7a1e3b8 100644
--- a/src/Magnum/Trade/AbstractMaterialData.cpp
+++ b/src/Magnum/Trade/AbstractMaterialData.cpp
@@ -38,20 +38,6 @@ AbstractMaterialData::AbstractMaterialData(const MaterialType type, const Flags
 
 AbstractMaterialData::~AbstractMaterialData() = default;
 
-Debug& operator<<(Debug& debug, const MaterialType value) {
-    debug << "Trade::MaterialType" << Debug::nospace;
-
-    switch(value) {
-        /* LCOV_EXCL_START */
-        #define _c(value) case MaterialType::value: return debug << "::" #value;
-        _c(Phong)
-        #undef _c
-        /* LCOV_EXCL_STOP */
-    }
-
-    return debug << "(" << Debug::nospace << reinterpret_cast<void*>(UnsignedByte(value)) << Debug::nospace << ")";
-}
-
 Debug& operator<<(Debug& debug, const AbstractMaterialData::Flag value) {
     debug << "Trade::AbstractMaterialData::Flag" << Debug::nospace;
 
diff --git a/src/Magnum/Trade/AbstractMaterialData.h b/src/Magnum/Trade/AbstractMaterialData.h
index 37bc0ae28..b833bf740 100644
--- a/src/Magnum/Trade/AbstractMaterialData.h
+++ b/src/Magnum/Trade/AbstractMaterialData.h
@@ -29,22 +29,10 @@
  * @brief Class @ref Magnum::Trade::AbstractMaterialData, enum @ref Magnum::Trade::MaterialType
  */
 
-#include <Corrade/Containers/EnumSet.h>
-
-#include "Magnum/Magnum.h"
-#include "Magnum/Trade/visibility.h"
+#include "Magnum/Trade/MaterialData.h"
 
 namespace Magnum { namespace Trade {
 
-/**
-@brief Material type
-
-@see @ref AbstractMaterialData::type()
-*/
-enum class MaterialType: UnsignedByte {
-    Phong       /**< Phong shading (see @ref PhongMaterialData) */
-};
-
 /**
 @brief Material alpha mode
 
@@ -165,9 +153,6 @@ class MAGNUM_TRADE_EXPORT AbstractMaterialData {
         const void* _importerState;
 };
 
-/** @debugoperatorenum{MaterialType} */
-MAGNUM_TRADE_EXPORT Debug& operator<<(Debug& debug, MaterialType value);
-
 /** @debugoperatorenum{MaterialAlphaMode} */
 MAGNUM_TRADE_EXPORT Debug& operator<<(Debug& debug, MaterialAlphaMode value);
 
diff --git a/src/Magnum/Trade/MaterialData.cpp b/src/Magnum/Trade/MaterialData.cpp
index b33c4b394..727a5a4a5 100644
--- a/src/Magnum/Trade/MaterialData.cpp
+++ b/src/Magnum/Trade/MaterialData.cpp
@@ -27,6 +27,7 @@
 
 #include <cstring>
 #include <algorithm>
+#include <Corrade/Containers/EnumSet.hpp>
 
 #include "Magnum/Math/Vector4.h"
 #include "Magnum/Math/Matrix.h"
@@ -126,7 +127,7 @@ const void* MaterialAttributeData::value() const {
     return _data.data + Implementation::MaterialAttributeDataSize - materialAttributeTypeSize(_data.type);
 }
 
-MaterialData::MaterialData(Containers::Array<MaterialAttributeData>&& data, const void* const importerState) noexcept: _data{std::move(data)}, _importerState{importerState} {
+MaterialData::MaterialData(const MaterialTypes types, Containers::Array<MaterialAttributeData>&& data, const void* const importerState) noexcept: _data{std::move(data)}, _types{types}, _importerState{importerState} {
     #ifndef CORRADE_NO_ASSERT
     /* Not checking what's already done in MaterialAttributeData constructor.
        Done before sorting so the index refers to the actual input index. */
@@ -155,9 +156,9 @@ MaterialData::MaterialData(Containers::Array<MaterialAttributeData>&& data, cons
     }
 }
 
-MaterialData::MaterialData(const std::initializer_list<MaterialAttributeData> data, const void* const importerState): MaterialData{Implementation::initializerListToArrayWithDefaultDeleter(data), importerState} {}
+MaterialData::MaterialData(const MaterialTypes types, const std::initializer_list<MaterialAttributeData> data, const void* const importerState): MaterialData{types, Implementation::initializerListToArrayWithDefaultDeleter(data), importerState} {}
 
-MaterialData::MaterialData(DataFlags, const Containers::ArrayView<const MaterialAttributeData> data, const void* const importerState) noexcept: _data{Containers::Array<MaterialAttributeData>{const_cast<MaterialAttributeData*>(data.data()), data.size(), [](MaterialAttributeData*, std::size_t){}}}, _importerState{importerState} {
+MaterialData::MaterialData(const MaterialTypes types, DataFlags, const Containers::ArrayView<const MaterialAttributeData> data, const void* const importerState) noexcept: _data{Containers::Array<MaterialAttributeData>{const_cast<MaterialAttributeData*>(data.data()), data.size(), [](MaterialAttributeData*, std::size_t){}}}, _types{types}, _importerState{importerState} {
     #ifndef CORRADE_NO_ASSERT
     /* Not checking what's already done in MaterialAttributeData constructor */
     for(std::size_t i = 0; i != _data.size(); ++i)
@@ -323,4 +324,24 @@ Debug& operator<<(Debug& debug, const MaterialAttributeType value) {
     return debug << "(" << Debug::nospace << reinterpret_cast<void*>(UnsignedShort(value)) << Debug::nospace << ")";
 }
 
+Debug& operator<<(Debug& debug, const MaterialType value) {
+    debug << "Trade::MaterialType" << Debug::nospace;
+
+    switch(value) {
+        /* LCOV_EXCL_START */
+        #define _c(value) case MaterialType::value: return debug << "::" #value;
+        _c(Phong)
+        #undef _c
+        /* LCOV_EXCL_STOP */
+    }
+
+    return debug << "(" << Debug::nospace << reinterpret_cast<void*>(UnsignedByte(value)) << Debug::nospace << ")";
+}
+
+Debug& operator<<(Debug& debug, const MaterialTypes value) {
+    return Containers::enumSetDebugOutput(debug, value, "Trade::MaterialTypes{}", {
+        MaterialType::Phong
+    });
+}
+
 }}
diff --git a/src/Magnum/Trade/MaterialData.h b/src/Magnum/Trade/MaterialData.h
index d5ada0477..be54b499f 100644
--- a/src/Magnum/Trade/MaterialData.h
+++ b/src/Magnum/Trade/MaterialData.h
@@ -507,6 +507,32 @@ class MAGNUM_TRADE_EXPORT MaterialAttributeData {
         static_assert(sizeof(Storage) == Implementation::MaterialAttributeDataSize, "something is off, huh");
 };
 
+/**
+@brief Material type
+
+@see @ref MaterialTypes, @ref MaterialData::types(),
+    @ref AbstractMaterialData::type()
+*/
+enum class MaterialType: UnsignedInt {
+    Phong = 1 << 0      /**< Phong shading */
+};
+
+/** @debugoperatorenum{MaterialType} */
+MAGNUM_TRADE_EXPORT Debug& operator<<(Debug& debug, MaterialType value);
+
+/**
+@brief Material types
+@m_since_latest
+
+@see @ref MaterialData::types()
+*/
+typedef Containers::EnumSet<MaterialType> MaterialTypes;
+
+CORRADE_ENUMSET_OPERATORS(MaterialTypes)
+
+/** @debugoperatorenum{MaterialTypes} */
+MAGNUM_TRADE_EXPORT Debug& operator<<(Debug& debug, MaterialTypes value);
+
 /**
 @brief Material data
 @m_since_latest
@@ -543,19 +569,23 @@ class MAGNUM_TRADE_EXPORT MaterialData {
     public:
         /**
          * @brief Construct
+         * @param types             Which material types are described by this
+         *      data. Can be an empty set.
          * @param data              Attribute data
          * @param importerState     Importer-specific state
          *
          * The @p data gets sorted by name internally, expecting no duplicates.
          */
-        explicit MaterialData(Containers::Array<MaterialAttributeData>&& data, const void* importerState = nullptr) noexcept;
+        explicit MaterialData(MaterialTypes types, Containers::Array<MaterialAttributeData>&& data, const void* importerState = nullptr) noexcept;
 
         /** @overload */
         /* Not noexcept because allocation happens inside */
-        explicit MaterialData(std::initializer_list<MaterialAttributeData> data, const void* importerState = nullptr);
+        explicit MaterialData(MaterialTypes types, std::initializer_list<MaterialAttributeData> data, const void* importerState = nullptr);
 
         /**
          * @brief Construct a non-owned material data
+         * @param types             Which material types are described by this
+         *      data. Can be an empty set.
          * @param dataFlags         Ignored. Used only for a safer distinction
          *      from the owning constructor.
          * @param data              Attribute data
@@ -564,7 +594,7 @@ class MAGNUM_TRADE_EXPORT MaterialData {
          * The @p data is expected to be already sorted by name, without
          * duplicates.
          */
-        explicit MaterialData(DataFlags dataFlags, Containers::ArrayView<const MaterialAttributeData> data, const void* importerState = nullptr) noexcept;
+        explicit MaterialData(MaterialTypes types, DataFlags dataFlags, Containers::ArrayView<const MaterialAttributeData> data, const void* importerState = nullptr) noexcept;
 
         ~MaterialData();
 
@@ -580,6 +610,14 @@ class MAGNUM_TRADE_EXPORT MaterialData {
         /** @brief Move assignment */
         MaterialData& operator=(MaterialData&&) noexcept;
 
+        /**
+         * @brief Material types
+         *
+         * Each type indicates that the material data can be interpreted as
+         * given type. For custom materials the set can also be empty.
+         */
+        MaterialTypes types() const { return _types; }
+
         /**
          * @brief Raw attribute data
          *
@@ -731,6 +769,7 @@ class MAGNUM_TRADE_EXPORT MaterialData {
         UnsignedInt attributeFor(Containers::StringView name) const;
 
         Containers::Array<MaterialAttributeData> _data;
+        MaterialTypes _types;
         const void* _importerState;
 };
 
diff --git a/src/Magnum/Trade/Test/MaterialDataTest.cpp b/src/Magnum/Trade/Test/MaterialDataTest.cpp
index 14260820a..913dcc176 100644
--- a/src/Magnum/Trade/Test/MaterialDataTest.cpp
+++ b/src/Magnum/Trade/Test/MaterialDataTest.cpp
@@ -97,6 +97,7 @@ class MaterialDataTest: public TestSuite::Tester {
         void debugAttributeType();
 
         void debugType();
+        void debugTypes();
         void debugFlag();
         void debugFlags();
         void debugAlphaMode();
@@ -186,6 +187,7 @@ MaterialDataTest::MaterialDataTest() {
               &MaterialDataTest::debugAttributeType,
 
               &MaterialDataTest::debugType,
+              &MaterialDataTest::debugTypes,
               &MaterialDataTest::debugFlag,
               &MaterialDataTest::debugFlags,
               &MaterialDataTest::debugAlphaMode,
@@ -422,13 +424,14 @@ void MaterialDataTest::constructAttributeWrongAccessType() {
 
 void MaterialDataTest::construct() {
     int state;
-    MaterialData data{{
+    MaterialData data{MaterialType::Phong, {
         {MaterialAttribute::DoubleSided, true},
         {MaterialAttribute::DiffuseTextureCoordinates, 5u},
         {"highlightColor", 0x335566ff_rgbaf},
         {MaterialAttribute::AmbientTextureMatrix, Matrix3::scaling({0.5f, 1.0f})}
     }, &state};
 
+    CORRADE_COMPARE(data.types(), MaterialType::Phong);
     CORRADE_COMPARE(data.attributeCount(), 4);
     CORRADE_COMPARE(data.data().size(), 4);
     CORRADE_COMPARE(data.importerState(), &state);
@@ -509,7 +512,7 @@ void MaterialDataTest::constructEmptyAttribute() {
 
     std::ostringstream out;
     Error redirectError{&out};
-    MaterialData{{
+    MaterialData{{}, {
         {"DiffuseTexture"_s, 12u},
         MaterialAttributeData{}
     }};
@@ -537,7 +540,7 @@ void MaterialDataTest::constructDuplicateAttribute() {
 
     std::ostringstream out;
     Error redirectError{&out};
-    MaterialData data{std::move(attributes)};
+    MaterialData data{{}, std::move(attributes)};
     /* Because with graceful asserts it doesn't exit on error, the assertion
        might get printed multiple times */
     CORRADE_COMPARE(Utility::String::partition(out.str(), '\n')[0], "Trade::MaterialData: duplicate attribute DiffuseTextureCoordinates");
@@ -549,7 +552,7 @@ void MaterialDataTest::constructFromImmutableSortedArray() {
         {"yay this is last"_s, Vector4{0.2f, 0.6f, 0.4f, 1.0f}}
     };
 
-    MaterialData data{Containers::Array<MaterialAttributeData>{const_cast<MaterialAttributeData*>(attributes), Containers::arraySize(attributes), [](MaterialAttributeData*, std::size_t) {}}};
+    MaterialData data{{}, Containers::Array<MaterialAttributeData>{const_cast<MaterialAttributeData*>(attributes), Containers::arraySize(attributes), [](MaterialAttributeData*, std::size_t) {}}};
 
     CORRADE_COMPARE(data.attributeCount(), 2);
     CORRADE_COMPARE(data.attributeName(0), "hello this is first");
@@ -567,9 +570,10 @@ void MaterialDataTest::constructNonOwned() {
     };
 
     int state;
-    MaterialData data{{}, attributes, &state};
+    MaterialData data{MaterialType::Phong, {}, attributes, &state};
 
     /* Expecting the same output as in construct() */
+    CORRADE_COMPARE(data.types(), MaterialType::Phong);
     CORRADE_COMPARE(data.attributeCount(), 4);
     CORRADE_COMPARE(data.data().size(), 4);
     CORRADE_COMPARE(data.data().data(), attributes);
@@ -598,7 +602,7 @@ void MaterialDataTest::constructNonOwnedEmptyAttribute() {
     std::ostringstream out;
     Error redirectError{&out};
     /* nullptr to avoid attributes interpreted as importerState */
-    MaterialData{{}, attributes, nullptr};
+    MaterialData{{}, {}, attributes, nullptr};
     CORRADE_COMPARE(out.str(), "Trade::MaterialData: attribute 1 doesn't specify anything\n");
 }
 
@@ -615,7 +619,7 @@ void MaterialDataTest::constructNonOwnedNotSorted() {
     std::ostringstream out;
     Error redirectError{&out};
     /* nullptr to avoid attributes interpreted as importerState */
-    MaterialData{{}, attributes, nullptr};
+    MaterialData{{}, {}, attributes, nullptr};
     CORRADE_COMPARE(out.str(), "Trade::MaterialData: DiffuseTexture has to be sorted before DiffuseTextureCoordinates if passing non-owned data\n");
 }
 
@@ -633,7 +637,7 @@ void MaterialDataTest::constructNonOwnedDuplicateAttribute() {
     std::ostringstream out;
     Error redirectError{&out};
     /* nullptr to avoid attributes interpreted as importerState */
-    MaterialData{{}, attributes, nullptr};
+    MaterialData{{}, {}, attributes, nullptr};
     CORRADE_COMPARE(out.str(), "Trade::MaterialData: duplicate attribute DiffuseTextureCoordinates\n");
 }
 
@@ -644,22 +648,24 @@ void MaterialDataTest::constructCopy() {
 
 void MaterialDataTest::constructMove() {
     int state;
-    MaterialData a{{
+    MaterialData a{MaterialType::Phong, {
         {MaterialAttribute::DoubleSided, true},
         {"boredomFactor", 5}
     }, &state};
 
     MaterialData b{std::move(a)};
     CORRADE_COMPARE(a.attributeCount(), 0);
+    CORRADE_COMPARE(b.types(), MaterialType::Phong);
     CORRADE_COMPARE(b.attributeCount(), 2);
     CORRADE_COMPARE(b.attributeName(0), "DoubleSided");
     CORRADE_COMPARE(b.importerState(), &state);
 
-    MaterialData c{{
+    MaterialData c{MaterialTypes{}, {
         {MaterialAttribute::AlphaMask, 0.5f}
     }};
     c = std::move(b);
     CORRADE_COMPARE(b.attributeCount(), 1);
+    CORRADE_COMPARE(c.types(), MaterialType::Phong);
     CORRADE_COMPARE(c.attributeCount(), 2);
     CORRADE_COMPARE(c.attributeName(0), "DoubleSided");
     CORRADE_COMPARE(c.importerState(), &state);
@@ -669,7 +675,7 @@ void MaterialDataTest::constructMove() {
 }
 
 void MaterialDataTest::accessOptional() {
-    MaterialData data{{
+    MaterialData data{{}, {
         {MaterialAttribute::AlphaMask, 0.5f},
         {MaterialAttribute::SpecularTexture, 3u}
     }};
@@ -698,7 +704,7 @@ void MaterialDataTest::accessOutOfBounds() {
     CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
     #endif
 
-    MaterialData data{{
+    MaterialData data{{}, {
         {MaterialAttribute::AlphaMask, 0.5f},
         {MaterialAttribute::SpecularTexture, 3u}
     }};
@@ -721,7 +727,7 @@ void MaterialDataTest::accessInvalidAttributeName() {
     CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
     #endif
 
-    MaterialData data{};
+    MaterialData data{{}, {}};
 
     std::ostringstream out;
     Error redirectError{&out};
@@ -765,7 +771,7 @@ void MaterialDataTest::accessNotFound() {
     CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
     #endif
 
-    MaterialData data{{
+    MaterialData data{{}, {
         {"DiffuseColor", 0xff3366aa_rgbaf}
     }};
 
@@ -789,7 +795,7 @@ void MaterialDataTest::accessWrongType() {
     CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
     #endif
 
-    MaterialData data{{
+    MaterialData data{{}, {
         {"DiffuseColor", 0xff3366aa_rgbaf}
     }};
 
@@ -815,7 +821,7 @@ void MaterialDataTest::accessWrongType() {
 }
 
 void MaterialDataTest::release() {
-    MaterialData data{{
+    MaterialData data{{}, {
         {"DiffuseColor", 0xff3366aa_rgbaf},
         {MaterialAttribute::NormalTexture, 0u}
     }};
@@ -1103,6 +1109,13 @@ void MaterialDataTest::debugType() {
     CORRADE_COMPARE(out.str(), "Trade::MaterialType::Phong Trade::MaterialType(0xbe)\n");
 }
 
+void MaterialDataTest::debugTypes() {
+    std::ostringstream out;
+
+    Debug{&out} << (MaterialType::Phong|MaterialType(0xe0)) << MaterialTypes{};
+    CORRADE_COMPARE(out.str(), "Trade::MaterialType::Phong|Trade::MaterialType(0xe0) Trade::MaterialTypes{}\n");
+}
+
 void MaterialDataTest::debugFlag() {
     std::ostringstream out;
 
diff --git a/src/Magnum/Trade/Trade.h b/src/Magnum/Trade/Trade.h
index 164ae036a..154dd4762 100644
--- a/src/Magnum/Trade/Trade.h
+++ b/src/Magnum/Trade/Trade.h
@@ -50,7 +50,7 @@ typedef CORRADE_DEPRECATED("use InputFileCallbackPolicy instead") InputFileCallb
 
 enum class MaterialAttribute: UnsignedInt;
 enum class MaterialAttributeType: UnsignedByte;
-enum class MaterialType: UnsignedByte;
+enum class MaterialType: UnsignedInt;
 enum class MaterialAlphaMode: UnsignedByte;
 class AbstractMaterialData;
 class MaterialAttributeData;