diff --git a/src/Magnum/Shapes/AbstractShape.cpp b/src/Magnum/Shapes/AbstractShape.cpp
index 913ed01e9..8bb10797a 100644
--- a/src/Magnum/Shapes/AbstractShape.cpp
+++ b/src/Magnum/Shapes/AbstractShape.cpp
@@ -27,6 +27,7 @@
 
 #include <Corrade/Utility/Debug.h>
 
+#include "Magnum/Shapes/Collision.h"
 #include "Magnum/Shapes/ShapeGroup.h"
 #include "Magnum/Shapes/Implementation/CollisionDispatch.h"
 
@@ -52,6 +53,10 @@ template<UnsignedInt dimensions> bool AbstractShape<dimensions>::collides(const
     return Implementation::collides(abstractTransformedShape(), other.abstractTransformedShape());
 }
 
+template<UnsignedInt dimensions> Collision<dimensions> AbstractShape<dimensions>::collision(const AbstractShape<dimensions>& other) const {
+    return Implementation::collision(abstractTransformedShape(), other.abstractTransformedShape());
+}
+
 template<UnsignedInt dimensions> void AbstractShape<dimensions>::markDirty() {
     if(group()) group()->setDirty();
 }
diff --git a/src/Magnum/Shapes/AbstractShape.h b/src/Magnum/Shapes/AbstractShape.h
index 2273944de..fdcb3a75c 100644
--- a/src/Magnum/Shapes/AbstractShape.h
+++ b/src/Magnum/Shapes/AbstractShape.h
@@ -102,6 +102,13 @@ template<UnsignedInt dimensions> class MAGNUM_SHAPES_EXPORT AbstractShape: publi
          */
         bool collides(const AbstractShape<dimensions>& other) const;
 
+        /**
+         * @brief Collision with other shape
+         *
+         * Default implementation returns empty collision.
+         */
+        Collision<dimensions> collision(const AbstractShape<dimensions>& other) const;
+
     protected:
         /** Marks also the group as dirty */
         void markDirty() override;
diff --git a/src/Magnum/Shapes/Implementation/CollisionDispatch.cpp b/src/Magnum/Shapes/Implementation/CollisionDispatch.cpp
index 621396a1b..11a76adcd 100644
--- a/src/Magnum/Shapes/Implementation/CollisionDispatch.cpp
+++ b/src/Magnum/Shapes/Implementation/CollisionDispatch.cpp
@@ -65,6 +65,21 @@ template<> bool collides(const AbstractShape<2>& a, const AbstractShape<2>& b) {
     return false;
 }
 
+template<> Collision<2> collision(const AbstractShape<2>& a, const AbstractShape<2>& b) {
+    if(a.type() < b.type()) return collision(b, a);
+
+    switch(UnsignedInt(a.type())*UnsignedInt(b.type())) {
+        #define _c(aType, aClass, bType, bClass) \
+            case UnsignedInt(ShapeDimensionTraits<2>::Type::aType)*UnsignedInt(ShapeDimensionTraits<2>::Type::bType): \
+                return static_cast<const Shape<aClass>&>(a).shape / static_cast<const Shape<bClass>&>(b).shape;
+        _c(Sphere, Sphere2D, Point, Point2D)
+        _c(Sphere, Sphere2D, Sphere, Sphere2D)
+        #undef _c
+    }
+
+    return {};
+}
+
 template<> bool collides(const AbstractShape<3>& a, const AbstractShape<3>& b) {
     if(a.type() < b.type()) return collides(b, a);
 
@@ -96,4 +111,19 @@ template<> bool collides(const AbstractShape<3>& a, const AbstractShape<3>& b) {
     return false;
 }
 
+template<> Collision<3> collision(const AbstractShape<3>& a, const AbstractShape<3>& b) {
+    if(a.type() < b.type()) return collision(b, a);
+
+    switch(UnsignedInt(a.type())*UnsignedInt(b.type())) {
+        #define _c(aType, aClass, bType, bClass) \
+            case UnsignedInt(ShapeDimensionTraits<3>::Type::aType)*UnsignedInt(ShapeDimensionTraits<3>::Type::bType): \
+                return static_cast<const Shape<aClass>&>(a).shape / static_cast<const Shape<bClass>&>(b).shape;
+        _c(Sphere, Sphere3D, Point, Point3D)
+        _c(Sphere, Sphere3D, Sphere, Sphere3D)
+        #undef _c
+    }
+
+    return {};
+}
+
 }}}
diff --git a/src/Magnum/Shapes/Implementation/CollisionDispatch.h b/src/Magnum/Shapes/Implementation/CollisionDispatch.h
index cd1dd564b..84d79aa2f 100644
--- a/src/Magnum/Shapes/Implementation/CollisionDispatch.h
+++ b/src/Magnum/Shapes/Implementation/CollisionDispatch.h
@@ -26,6 +26,7 @@
 */
 
 #include "Magnum/Types.h"
+#include "Magnum/Shapes/Shapes.h"
 
 namespace Magnum { namespace Shapes { namespace Implementation {
 
@@ -40,8 +41,11 @@ multiply the two numbers together and switch() on the result. Because of
 multiplying two prime numbers, there is no ambiguity (the result is unique for
 each combination).
 */
+
 template<UnsignedInt dimensions> bool collides(const AbstractShape<dimensions>& a, const AbstractShape<dimensions>& b);
 
+template<UnsignedInt dimensions> Collision<dimensions> collision(const AbstractShape<dimensions>& a, const AbstractShape<dimensions>& b);
+
 }}}
 
 #endif
diff --git a/src/Magnum/Shapes/Test/ShapeTest.cpp b/src/Magnum/Shapes/Test/ShapeTest.cpp
index 9f88909c4..e9a74d915 100644
--- a/src/Magnum/Shapes/Test/ShapeTest.cpp
+++ b/src/Magnum/Shapes/Test/ShapeTest.cpp
@@ -42,6 +42,7 @@ class ShapeTest: public TestSuite::Tester {
 
         void clean();
         void collides();
+        void collision();
         void firstCollision();
         void shapeGroup();
 };
@@ -54,6 +55,7 @@ typedef SceneGraph::Object<SceneGraph::MatrixTransformation3D> Object3D;
 ShapeTest::ShapeTest() {
     addTests({&ShapeTest::clean,
               &ShapeTest::collides,
+              &ShapeTest::collision,
               &ShapeTest::firstCollision,
               &ShapeTest::shapeGroup});
 }
@@ -137,6 +139,49 @@ void ShapeTest::collides() {
     }
 }
 
+void ShapeTest::collision() {
+    Scene3D scene;
+    ShapeGroup3D shapes;
+    Object3D a(&scene);
+    Shape<Shapes::Sphere3D> aShape(a, {{1.0f, -2.0f, 3.0f}, 1.5f}, &shapes);
+
+    {
+        /* Collision with point inside the sphere */
+        Shape<Shapes::Point3D> aShape2(a, {{1.0f, -2.0f, 3.0f}}, &shapes);
+        shapes.setClean();
+        const Collision3D collision = aShape.collision(aShape2);
+        CORRADE_VERIFY(collision);
+        CORRADE_COMPARE(collision.position(), Vector3(1.0f, -2.0f, 3.0f));
+    } {
+        /* No collision with point inside the sphere, but not in the same group */
+        ShapeGroup3D shapes2;
+        Shape<Shapes::Point3D> aShape3(a, {{1.0f, -2.0f, 3.0f}}, &shapes2);
+        shapes2.setClean();
+        CORRADE_VERIFY(!aShape.collision(aShape3));
+    } {
+        CORRADE_EXPECT_FAIL("Should cross-scene collision work or not?");
+        /* No collision with point inside the sphere, but not in the same scene */
+        Scene3D scene2;
+        Object3D c(&scene2);
+        Shape<Shapes::Point3D> cShape(c, {{1.0f, -2.0f, 3.0f}}, &shapes);
+        shapes.setClean();
+        CORRADE_VERIFY(!aShape.collision(cShape));
+    } {
+        /* No collision with point outside of the sphere */
+        Object3D b(&scene);
+        Shape<Shapes::Point3D> bShape(b, {{3.0f, -2.0f, 3.0f}}, &shapes);
+        shapes.setClean();
+        CORRADE_VERIFY(!aShape.collision(bShape));
+
+        /* Move point inside the sphere -- collision */
+        b.translate(Vector3::xAxis(-1.0f));
+        shapes.setClean();
+        const Collision3D collision = aShape.collision(bShape);
+        CORRADE_VERIFY(collision);
+        CORRADE_COMPARE(collision.position(), Vector3(2.0f, -2.0f, 3.0f));
+    }
+}
+
 void ShapeTest::firstCollision() {
     Scene3D scene;
     ShapeGroup3D shapes;