diff --git a/src/Math/Functions.h b/src/Math/Functions.h
index c80fd1eab..ad9066195 100644
--- a/src/Math/Functions.h
+++ b/src/Math/Functions.h
@@ -20,6 +20,8 @@
 #include <limits>
 #include <algorithm>
 
+#include "Math/Vector.h"
+
 #include "magnumVisibility.h"
 
 /** @file
@@ -78,6 +80,73 @@ std::uint32_t MAGNUM_EXPORT log2(std::uint32_t number);
  */
 std::uint32_t MAGNUM_EXPORT log(std::uint32_t base, std::uint32_t number);
 
+/**
+@{ @name Scalar/vector functions
+
+These functions are overloaded for both scalar and vector types. Scalar
+versions function exactly as their possible STL equivalents, vector overloads
+perform the operations component-wise.
+*/
+
+/**
+@brief Minimum
+
+@see min(), clamp()
+*/
+#ifdef DOXYGEN_GENERATING_OUTPUT
+template<class T> inline T min(T a, T b);
+#else
+template<class T> inline typename std::enable_if<std::is_arithmetic<T>::value, T>::type min(T a, T b) {
+    return std::min(a, b);
+}
+template<std::size_t size, class T> inline Vector<size, T> min(const Vector<size, T>& a, const Vector<size, T>& b) {
+    Vector<size, T> out;
+    for(std::size_t i = 0; i != size; ++i)
+        out[i] = std::min(a[i], b[i]);
+    return out;
+}
+#endif
+
+/**
+@brief Maximum
+
+@see max(), clamp()
+*/
+#ifdef DOXYGEN_GENERATING_OUTPUT
+template<class T> inline T max(const T& a, const T& b);
+#else
+template<class T> inline typename std::enable_if<std::is_arithmetic<T>::value, T>::type max(T a, T b) {
+    return std::max(a, b);
+}
+template<std::size_t size, class T> Vector<size, T> max(const Vector<size, T>& a, const Vector<size, T>& b) {
+    Vector<size, T> out;
+    for(std::size_t i = 0; i != size; ++i)
+        out[i] = std::max(a[i], b[i]);
+    return out;
+}
+#endif
+
+/**
+@brief Clamp value
+
+Values smaller than @p min are set to @p min, values larger than @p max are
+set to @p max.
+@see min(), max()
+*/
+#ifdef DOXYGEN_GENERATING_OUTPUT
+template<class T, class U> inline T clamp(const T& value, U min, U max);
+#else
+template<class T> inline typename std::enable_if<std::is_arithmetic<T>::value, T>::type clamp(T value, T min, T max) {
+    return std::min(std::max(value, min), max);
+}
+template<std::size_t size, class T> Vector<size, T> clamp(const Vector<size, T>& value, T min, T max) {
+    Vector<size, T> out;
+    for(std::size_t i = 0; i != size; ++i)
+        out[i] = std::min(std::max(value[i], min), max);
+    return out;
+}
+#endif
+
 /**
 @brief Normalize integral value
 
@@ -134,10 +203,7 @@ template<class Integral, class FloatingPoint> inline constexpr typename std::ena
 }
 #endif
 
-/** @brief Clamp value */
-template<class T> inline T clamp(T value, T min, T max) {
-    return std::min(std::max(value, min), max);
-}
+/*@}*/
 
 }}
 
diff --git a/src/Math/Test/FunctionsTest.cpp b/src/Math/Test/FunctionsTest.cpp
index 9b55ae7e2..eff4ff119 100644
--- a/src/Math/Test/FunctionsTest.cpp
+++ b/src/Math/Test/FunctionsTest.cpp
@@ -16,6 +16,7 @@
 #include <TestSuite/Tester.h>
 
 #include "Math/Functions.h"
+#include "Math/Vector3.h"
 
 namespace Magnum { namespace Math { namespace Test {
 
@@ -23,31 +24,57 @@ class FunctionsTest: public Corrade::TestSuite::Tester {
     public:
         FunctionsTest();
 
+        void min();
+        void max();
+        void clamp();
         void normalizeUnsigned();
         void normalizeSigned();
         void denormalizeUnsigned();
         void denormalizeSigned();
         void renormalizeUnsinged();
         void renormalizeSinged();
-        void clamp();
+
         void pow();
         void log();
         void log2();
 };
 
+typedef Math::Vector3<float> Vector3;
+typedef Math::Vector3<std::int32_t> Vector3i;
+
 FunctionsTest::FunctionsTest() {
-    addTests(&FunctionsTest::normalizeUnsigned,
+    addTests(&FunctionsTest::min,
+             &FunctionsTest::max,
+             &FunctionsTest::clamp,
+             &FunctionsTest::normalizeUnsigned,
              &FunctionsTest::normalizeSigned,
              &FunctionsTest::denormalizeUnsigned,
              &FunctionsTest::denormalizeSigned,
              &FunctionsTest::renormalizeUnsinged,
              &FunctionsTest::renormalizeSinged,
-             &FunctionsTest::clamp,
              &FunctionsTest::pow,
              &FunctionsTest::log,
              &FunctionsTest::log2);
 }
 
+void FunctionsTest::min() {
+    CORRADE_COMPARE(Math::min(5, 9), 5);
+    CORRADE_COMPARE(Math::min(Vector3i(5, -3, 2), Vector3i(9, -5, 18)), Vector3i(5, -5, 2));
+}
+
+void FunctionsTest::max() {
+    CORRADE_COMPARE(Math::max(5, 9), 9);
+    CORRADE_COMPARE(Math::max(Vector3i(5, -3, 2), Vector3i(9, -5, 18)), Vector3i(9, -3, 18));
+}
+
+void FunctionsTest::clamp() {
+    CORRADE_COMPARE(Math::clamp(0.5f, -1.0f, 5.0f), 0.5f);
+    CORRADE_COMPARE(Math::clamp(-1.6f, -1.0f, 5.0f), -1.0f);
+    CORRADE_COMPARE(Math::clamp(9.5f, -1.0f, 5.0f), 5.0f);
+
+    CORRADE_COMPARE(Math::clamp(Vector3(0.5f, -1.6f, 9.5f), -1.0f, 5.0f), Vector3(0.5f, -1.0f, 5.0f));
+}
+
 void FunctionsTest::normalizeUnsigned() {
     CORRADE_COMPARE((Math::normalize<float, std::uint8_t>(0)), 0.0f);
     CORRADE_COMPARE((Math::normalize<float, std::uint8_t>(255)), 1.0f);
@@ -156,12 +183,6 @@ void FunctionsTest::renormalizeSinged() {
     CORRADE_COMPARE(Math::normalize<long double>(Math::denormalize<std::int64_t>(1.0l)), 1.0l);
 }
 
-void FunctionsTest::clamp() {
-    CORRADE_COMPARE(Math::clamp(0.5f, -1.0f, 5.0f), 0.5f);
-    CORRADE_COMPARE(Math::clamp(-1.6f, -1.0f, 5.0f), -1.0f);
-    CORRADE_COMPARE(Math::clamp(9.5f, -1.0f, 5.0f), 5.0f);
-}
-
 void FunctionsTest::pow() {
     CORRADE_COMPARE(Math::pow<10>(2ul), 1024ul);
     CORRADE_COMPARE(Math::pow<0>(3ul), 1ul);