diff --git a/src/Magnum/Math/CMakeLists.txt b/src/Magnum/Math/CMakeLists.txt
index fa77b2b50..2f5cec82e 100644
--- a/src/Magnum/Math/CMakeLists.txt
+++ b/src/Magnum/Math/CMakeLists.txt
@@ -48,6 +48,7 @@ set(MagnumMath_HEADERS
     Packing.h
     Range.h
     RectangularMatrix.h
+    Simd.h
     StrictWeakOrdering.h
     Swizzle.h
     Tags.h
diff --git a/src/Magnum/Math/Simd.h b/src/Magnum/Math/Simd.h
new file mode 100644
index 000000000..9e28a94c6
--- /dev/null
+++ b/src/Magnum/Math/Simd.h
@@ -0,0 +1,148 @@
+#ifndef Magnum_Math_Simd_h
+#define Magnum_Math_Simd_h
+/*
+    This file is part of Magnum.
+
+    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019
+              Vladimír Vondruš <mosra@centrum.cz>
+
+    Permission is hereby granted, free of charge, to any person obtaining a
+    copy of this software and associated documentation files (the "Software"),
+    to deal in the Software without restriction, including without limitation
+    the rights to use, copy, modify, merge, publish, distribute, sublicense,
+    and/or sell copies of the Software, and to permit persons to whom the
+    Software is furnished to do so, subject to the following conditions:
+
+    The above copyright notice and this permission notice shall be included
+    in all copies or substantial portions of the Software.
+
+    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+    DEALINGS IN THE SOFTWARE.
+*/
+
+/** @file
+ * @brief Namespace @ref Magnum::Math::Simd
+ */
+
+/** @namespace Magnum::Math::Simd
+@brief SIMD dispatch tags
+
+Tags for dispatching to particular SIMD-optimized versions of batch math
+algorithms.
+
+This library is built as part of Magnum by default. To use this library with
+CMake, you need to find the `Magnum` package and link to the `Magnum::Magnum`
+target:
+
+@code{.cmake}
+find_package(Magnum REQUIRED)
+
+# ...
+target_link_libraries(your-app Magnum::Magnum)
+@endcode
+
+See @ref building and @ref cmake for more information.
+*/
+namespace Magnum { namespace Math { namespace Simd {
+
+/**
+@brief No SIMD acceleration tag type
+
+Used to distinguish algorithms that have no explicit SIMD optimizations, apart
+from compiler magic.
+@see @ref None
+*/
+/* Explicit constructor to avoid ambiguous calls when using {} */
+struct NoneT {
+    #ifndef DOXYGEN_GENERATING_OUTPUT
+    struct Init{};
+    constexpr explicit NoneT(Init) {}
+    #endif
+};
+
+/**
+@brief SSE2 SIMD acceleration tag type
+
+Used to distinguish algorithms that use at most the
+[SSE2](https://en.wikipedia.org/wiki/SSE2) instruction set.
+@see @ref Sse2
+*/
+/* Explicit constructor to avoid ambiguous calls when using {} */
+struct Sse2T {
+    #ifndef DOXYGEN_GENERATING_OUTPUT
+    struct Init{};
+    constexpr explicit Sse2T(Init) {}
+    #endif
+};
+
+/**
+@brief SSE4.1 SIMD acceleration tag type
+
+Used to distinguish algorithms that use at most the
+[SSE4.1](https://en.wikipedia.org/wiki/SSE4#SSE4.1) instruction set.
+@see @ref Sse41
+*/
+/* Explicit constructor to avoid ambiguous calls when using {} */
+struct Sse41T {
+    #ifndef DOXYGEN_GENERATING_OUTPUT
+    struct Init{};
+    constexpr explicit Sse41T(Init) {}
+    #endif
+};
+
+/**
+@brief AVX2 SIMD acceleration tag type
+
+Used to distinguish algorithms that use at most the
+[AVX2](https://en.wikipedia.org/wiki/Advanced_Vector_Extensions#AVX2)
+instruction set.
+@see @ref Avx2
+*/
+/* Explicit constructor to avoid ambiguous calls when using {} */
+struct Avx2T {
+    #ifndef DOXYGEN_GENERATING_OUTPUT
+    struct Init{};
+    constexpr explicit Avx2T(Init) {}
+    #endif
+};
+
+/**
+@brief No SIMD acceleration tag
+
+Use for selecting algorithms with no explicit SIMD optimizations.
+*/
+constexpr NoneT None{NoneT::Init{}};
+
+/**
+@brief SSE2 SIMD acceleration tag
+
+Use for selecting algorithms that use at most the
+[SSE2](https://en.wikipedia.org/wiki/SSE2) instruction set.
+*/
+constexpr Sse2T Sse2{Sse2T::Init{}};
+
+/**
+@brief SSE4.1 SIMD acceleration tag
+
+Use for selecting algorithms that use at most the
+[SSE4.1](https://en.wikipedia.org/wiki/SSE4#SSE4.1) instruction set.
+*/
+constexpr Sse41T Sse41{Sse41T::Init{}};
+
+/**
+@brief AVX2 SIMD acceleration tag type
+
+Use for selecting algorithms that use at most the
+[AVX2](https://en.wikipedia.org/wiki/Advanced_Vector_Extensions#AVX2)
+instruction set.
+*/
+constexpr Avx2T Avx2{Avx2T::Init{}};
+
+}}}
+
+#endif