diff --git a/src/Magnum/Trade/AbstractImporter.cpp b/src/Magnum/Trade/AbstractImporter.cpp
index 337b8578e1..28439b2d7b 100644
--- a/src/Magnum/Trade/AbstractImporter.cpp
+++ b/src/Magnum/Trade/AbstractImporter.cpp
@@ -38,6 +38,7 @@
 #include "Magnum/Trade/CameraData.h"
 #include "Magnum/Trade/ImageData.h"
 #include "Magnum/Trade/LightData.h"
+#include "Magnum/Trade/MeshData.h"
 #include "Magnum/Trade/MeshData2D.h"
 #include "Magnum/Trade/MeshData3D.h"
 #include "Magnum/Trade/ObjectData2D.h"
@@ -402,6 +403,38 @@ Containers::Pointer<ObjectData3D> AbstractImporter::doObject3D(UnsignedInt) {
     CORRADE_ASSERT(false, "Trade::AbstractImporter::object3D(): not implemented", {});
 }
 
+UnsignedInt AbstractImporter::meshCount() const {
+    CORRADE_ASSERT(isOpened(), "Trade::AbstractImporter::meshCount(): no file opened", {});
+    return doMeshCount();
+}
+
+UnsignedInt AbstractImporter::doMeshCount() const { return 0; }
+
+Int AbstractImporter::meshForName(const std::string& name) {
+    CORRADE_ASSERT(isOpened(), "Trade::AbstractImporter::meshForName(): no file opened", {});
+    return doMeshForName(name);
+}
+
+Int AbstractImporter::doMeshForName(const std::string&) { return -1; }
+
+std::string AbstractImporter::meshName(const UnsignedInt id) {
+    CORRADE_ASSERT(isOpened(), "Trade::AbstractImporter::meshName(): no file opened", {});
+    CORRADE_ASSERT(id < doMeshCount(), "Trade::AbstractImporter::meshName(): index" << id << "out of range for" << doMeshCount() << "entries", {});
+    return doMeshName(id);
+}
+
+std::string AbstractImporter::doMeshName(UnsignedInt) { return {}; }
+
+Containers::Optional<MeshData> AbstractImporter::mesh(const UnsignedInt id) {
+    CORRADE_ASSERT(isOpened(), "Trade::AbstractImporter::mesh(): no file opened", {});
+    CORRADE_ASSERT(id < doMeshCount(), "Trade::AbstractImporter::mesh(): index" << id << "out of range for" << doMeshCount() << "entries", {});
+    return doMesh(id);
+}
+
+Containers::Optional<MeshData> AbstractImporter::doMesh(UnsignedInt) {
+    CORRADE_ASSERT(false, "Trade::AbstractImporter::mesh(): not implemented", {});
+}
+
 UnsignedInt AbstractImporter::mesh2DCount() const {
     CORRADE_ASSERT(isOpened(), "Trade::AbstractImporter::mesh2DCount(): no file opened", {});
     return doMesh2DCount();
diff --git a/src/Magnum/Trade/AbstractImporter.h b/src/Magnum/Trade/AbstractImporter.h
index ef9c3624a0..773ca8d25e 100644
--- a/src/Magnum/Trade/AbstractImporter.h
+++ b/src/Magnum/Trade/AbstractImporter.h
@@ -117,8 +117,8 @@ expose internal state through various accessors:
     imported by @ref image1D(), @ref image2D() or @ref image3D()
 -   @ref LightData::importerState() can expose importer state for a light
     imported by @ref light()
--   @ref MeshData3D::importerState() can expose importer state for a mesh
-    imported by @ref mesh2D() or @ref mesh3D()
+-   @ref MeshData::importerState() can expose importer state for a mesh
+    imported by @ref mesh()
 -   @ref ObjectData3D::importerState() can expose importer state for an object
     imported by @ref object2D() or @ref object3D()
 -   @ref SceneData::importerState() can expose importer state for a scene
@@ -650,6 +650,40 @@ class MAGNUM_TRADE_EXPORT AbstractImporter: public PluginManager::AbstractManagi
          */
         Containers::Pointer<ObjectData3D> object3D(UnsignedInt id);
 
+        /**
+         * @brief Mesh count
+         *
+         * Expects that a file is opened.
+         */
+        UnsignedInt meshCount() const;
+
+        /**
+         * @brief Mesh ID for given name
+         *
+         * If no mesh for given name exists, returns @cpp -1 @ce. Expects that
+         * a file is opened.
+         * @see @ref meshName()
+         */
+        Int meshForName(const std::string& name);
+
+        /**
+         * @brief Mesh name
+         * @param id        Mesh ID, from range [0, @ref meshCount()).
+         *
+         * Expects that a file is opened.
+         * @see @ref meshForName()
+         */
+        std::string meshName(UnsignedInt id);
+
+        /**
+         * @brief Mesh
+         * @param id        Mesh ID, from range [0, @ref meshCount()).
+         *
+         * Returns given mesh or @ref Containers::NullOpt if importing failed.
+         * Expects that a file is opened.
+         */
+        Containers::Optional<MeshData> mesh(UnsignedInt id);
+
         /**
          * @brief Two-dimensional mesh count
          *
@@ -1097,6 +1131,30 @@ class MAGNUM_TRADE_EXPORT AbstractImporter: public PluginManager::AbstractManagi
         /** @brief Implementation for @ref object3D() */
         virtual Containers::Pointer<ObjectData3D> doObject3D(UnsignedInt id);
 
+        /**
+         * @brief Implementation for @ref meshCount()
+         *
+         * Default implementation returns @cpp 0 @ce.
+         */
+        virtual UnsignedInt doMeshCount() const;
+
+        /**
+         * @brief Implementation for @ref meshForName()
+         *
+         * Default implementation returns @cpp -1 @ce.
+         */
+        virtual Int doMeshForName(const std::string& name);
+
+        /**
+         * @brief Implementation for @ref meshName()
+         *
+         * Default implementation returns empty string.
+         */
+        virtual std::string doMeshName(UnsignedInt id);
+
+        /** @brief Implementation for @ref mesh() */
+        virtual Containers::Optional<MeshData> doMesh(UnsignedInt id);
+
         /**
          * @brief Implementation for @ref mesh2DCount()
          *
diff --git a/src/Magnum/Trade/Test/AbstractImporterTest.cpp b/src/Magnum/Trade/Test/AbstractImporterTest.cpp
index e8415339e6..ce3c64b16e 100644
--- a/src/Magnum/Trade/Test/AbstractImporterTest.cpp
+++ b/src/Magnum/Trade/Test/AbstractImporterTest.cpp
@@ -37,6 +37,7 @@
 #include "Magnum/Trade/CameraData.h"
 #include "Magnum/Trade/ImageData.h"
 #include "Magnum/Trade/LightData.h"
+#include "Magnum/Trade/MeshData.h"
 #include "Magnum/Trade/MeshData2D.h"
 #include "Magnum/Trade/MeshData3D.h"
 #include "Magnum/Trade/MeshObjectData2D.h"
@@ -156,6 +157,18 @@ struct AbstractImporterTest: TestSuite::Tester {
     void object3DNoFile();
     void object3DOutOfRange();
 
+    void mesh();
+    void meshCountNotImplemented();
+    void meshCountNoFile();
+    void meshForNameNotImplemented();
+    void meshForNameNoFile();
+    void meshNameNotImplemented();
+    void meshNameNoFile();
+    void meshNameOutOfRange();
+    void meshNotImplemented();
+    void meshNoFile();
+    void meshOutOfRange();
+
     void mesh2D();
     void mesh2DCountNotImplemented();
     void mesh2DCountNoFile();
@@ -356,6 +369,18 @@ AbstractImporterTest::AbstractImporterTest() {
               &AbstractImporterTest::object3DNoFile,
               &AbstractImporterTest::object3DOutOfRange,
 
+              &AbstractImporterTest::mesh,
+              &AbstractImporterTest::meshCountNotImplemented,
+              &AbstractImporterTest::meshCountNoFile,
+              &AbstractImporterTest::meshForNameNotImplemented,
+              &AbstractImporterTest::meshForNameNoFile,
+              &AbstractImporterTest::meshNameNotImplemented,
+              &AbstractImporterTest::meshNameNoFile,
+              &AbstractImporterTest::meshNameOutOfRange,
+              &AbstractImporterTest::meshNotImplemented,
+              &AbstractImporterTest::meshNoFile,
+              &AbstractImporterTest::meshOutOfRange,
+
               &AbstractImporterTest::mesh2D,
               &AbstractImporterTest::mesh2DCountNotImplemented,
               &AbstractImporterTest::mesh2DCountNoFile,
@@ -2019,6 +2044,175 @@ void AbstractImporterTest::object3DOutOfRange() {
     CORRADE_COMPARE(out.str(), "Trade::AbstractImporter::object3D(): index 8 out of range for 8 entries\n");
 }
 
+void AbstractImporterTest::mesh() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return true; }
+        void doClose() override {}
+
+        UnsignedInt doMeshCount() const override { return 8; }
+        Int doMeshForName(const std::string& name) override {
+            if(name == "eighth") return 7;
+            else return -1;
+        }
+        std::string doMeshName(UnsignedInt id) override {
+            if(id == 7) return "eighth";
+            else return {};
+        }
+        Containers::Optional<MeshData> doMesh(UnsignedInt id) override {
+            if(id == 7) return MeshData{{}, {}, &state};
+            else return {};
+        }
+    } importer;
+
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    CORRADE_COMPARE(importer.meshCount(), 8);
+    CORRADE_COMPARE(importer.meshForName("eighth"), 7);
+    CORRADE_COMPARE(importer.meshName(7), "eighth");
+
+    auto data = importer.mesh(7);
+    CORRADE_VERIFY(data);
+    CORRADE_COMPARE(data->importerState(), &state);
+}
+
+void AbstractImporterTest::meshCountNotImplemented() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return true; }
+        void doClose() override {}
+    } importer;
+
+    CORRADE_COMPARE(importer.meshCount(), 0);
+}
+
+void AbstractImporterTest::meshCountNoFile() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return false; }
+        void doClose() override {}
+    } importer;
+
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    importer.meshCount();
+    CORRADE_COMPARE(out.str(), "Trade::AbstractImporter::meshCount(): no file opened\n");
+}
+
+void AbstractImporterTest::meshForNameNotImplemented() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return true; }
+        void doClose() override {}
+    } importer;
+
+    CORRADE_COMPARE(importer.meshForName(""), -1);
+}
+
+void AbstractImporterTest::meshForNameNoFile() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return false; }
+        void doClose() override {}
+    } importer;
+
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    importer.meshForName("");
+    CORRADE_COMPARE(out.str(), "Trade::AbstractImporter::meshForName(): no file opened\n");
+}
+
+void AbstractImporterTest::meshNameNotImplemented() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return true; }
+        void doClose() override {}
+
+        UnsignedInt doMeshCount() const override { return 8; }
+    } importer;
+
+    CORRADE_COMPARE(importer.meshName(7), "");
+}
+
+void AbstractImporterTest::meshNameNoFile() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return false; }
+        void doClose() override {}
+    } importer;
+
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    importer.meshName(42);
+    CORRADE_COMPARE(out.str(), "Trade::AbstractImporter::meshName(): no file opened\n");
+}
+
+void AbstractImporterTest::meshNameOutOfRange() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return true; }
+        void doClose() override {}
+
+        UnsignedInt doMeshCount() const override { return 8; }
+    } importer;
+
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    importer.meshName(8);
+    CORRADE_COMPARE(out.str(), "Trade::AbstractImporter::meshName(): index 8 out of range for 8 entries\n");
+}
+
+void AbstractImporterTest::meshNotImplemented() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return true; }
+        void doClose() override {}
+
+        UnsignedInt doMeshCount() const override { return 8; }
+    } importer;
+
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    importer.mesh(7);
+    CORRADE_COMPARE(out.str(), "Trade::AbstractImporter::mesh(): not implemented\n");
+}
+
+void AbstractImporterTest::meshNoFile() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return false; }
+        void doClose() override {}
+    } importer;
+
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    importer.mesh(42);
+    CORRADE_COMPARE(out.str(), "Trade::AbstractImporter::mesh(): no file opened\n");
+}
+
+void AbstractImporterTest::meshOutOfRange() {
+    struct: AbstractImporter {
+        Features doFeatures() const override { return {}; }
+        bool doIsOpened() const override { return true; }
+        void doClose() override {}
+
+        UnsignedInt doMeshCount() const override { return 8; }
+    } importer;
+
+    std::ostringstream out;
+    Error redirectError{&out};
+
+    importer.mesh(8);
+    CORRADE_COMPARE(out.str(), "Trade::AbstractImporter::mesh(): index 8 out of range for 8 entries\n");
+}
+
 void AbstractImporterTest::mesh2D() {
     struct: AbstractImporter {
         Features doFeatures() const override { return {}; }