diff --git a/source/World.cpp b/source/World.cpp
index 3ad2074..3c0f61c 100755
--- a/source/World.cpp
+++ b/source/World.cpp
@@ -8,6 +8,7 @@
 #include "World.h"
 
 #include <algorithm>
+#include <assert.h>
 
 #include <Thor/Vectors.hpp>
 
@@ -40,14 +41,97 @@ World::remove(std::shared_ptr<Sprite> drawable) {
 void
 World::step(int elapsed) {
 	for (auto v = mDrawables.begin(); v != mDrawables.end(); v++) {
-		for (auto item = v->second.begin(); item != v->second.end(); item++) {
-			sf::Vector2f speed = (*item)->getSpeed();
+		for (auto spriteA : v->second) {
+			sf::Vector2f speed = spriteA->getSpeed();
 			speed *= elapsed / 1000.0f;
-			(*item)->setPosition((*item)->getPosition() + speed);
+			bool overlap = false;
+			for (auto w = mDrawables.begin(); w != mDrawables.end(); w++) {
+				for (auto spriteB : w->second) {
+					if (spriteA == spriteB) {
+						continue;
+					}
+					if (!spriteA->collisionEnabled(spriteB->getCategory()) || !spriteB->collisionEnabled(spriteA->getCategory())) {
+						continue;
+					}
+					if (testCollision(spriteA, spriteB, elapsed)) {
+						spriteA->onCollide(spriteB);
+						overlap = true;
+					}
+				}
+			}
+			if (!overlap) {
+				spriteA->setPosition(spriteA->getPosition() + speed);
+			}
 		}
 	}
 }
 
+/**
+ * Tests for collisions using Seperating Axis Theorem (SAT).
+ *
+ * http://www.metanetsoftware.com/technique/tutorialA.html
+ *
+ * @param spriteA, spriteB Pair of sprites which to test for collision/overlapping.
+ * @param elapsed Time elapsed in this step.
+ * @return True if both sprites will be overlapping after their current movement.
+ */
+bool
+World::testCollision(std::shared_ptr<Sprite> spriteA,
+		std::shared_ptr<Sprite> spriteB, int elapsed) const {
+	// circle-circle collision
+	if ((spriteA->mShape.type == Sprite::Shape::Type::CIRCLE) &&
+			(spriteB->mShape.type == Sprite::Shape::Type::CIRCLE)) {
+
+		sf::Vector2f axis = spriteA->getPosition() - spriteB->getPosition();
+		// If both objects are at the exact same position, allow any movement for unstucking.
+		if (axis == sf::Vector2f()) {
+			return true;
+		}
+		axis = thor::unitVector(axis);
+		float centerA = thor::dotProduct(axis, spriteA->getPosition());
+		float radiusA = std::static_pointer_cast<sf::CircleShape>(spriteA->mShape.shape)->getRadius();
+		float movementA = thor::dotProduct(axis, spriteA->getSpeed() * (elapsed / 1000.0f));
+		float centerB = thor::dotProduct(axis, spriteB->getPosition());
+		float radiusB = std::static_pointer_cast<sf::CircleShape>(spriteB->mShape.shape)->getRadius();
+		float movementB = thor::dotProduct(axis, spriteB->getSpeed() * (elapsed / 1000.0f));
+
+		// Allow movement if sprites are moving apart.
+		return Interval(centerA, radiusA).getOverlap(Interval(centerB, radiusB)).getLength() <
+				Interval(centerA + movementA, radiusA).getOverlap(Interval(centerB + movementB, radiusB)).getLength();
+	}
+	// circle-rect collision
+	if (((spriteA->mShape.type == Sprite::Shape::Type::CIRCLE) &&
+			(spriteB->mShape.type == Sprite::Shape::Type::RECTANGLE)) ||
+			((spriteA->mShape.type == Sprite::Shape::Type::RECTANGLE) &&
+			(spriteB->mShape.type == Sprite::Shape::Type::CIRCLE)))	{
+		std::shared_ptr<Sprite> circle = spriteA;
+		std::shared_ptr<Sprite> rect = spriteB;
+		if (circle->mShape.type != Sprite::Shape::Type::CIRCLE) {
+			std::swap(circle, rect);
+		}
+		float radius = std::static_pointer_cast<sf::CircleShape>(circle->mShape.shape)->getRadius();
+		sf::Vector2f size = rect->getSize();
+		sf::Vector2f circlePos = circle->getPosition();
+		sf::Vector2f rectPos = rect->getPosition();
+		// Only circle movement as rectangles don't move.
+		sf::Vector2f circleMovement = circle->getSpeed() * (elapsed / 1000.0f);
+
+		// We assume that rectangles are always axis aligned.
+		float overlapNoMovementX = Interval(circlePos.x, radius)
+								.getOverlap(Interval (rectPos.x, (size.x / 2))).getLength();
+		float overlapMovementX = Interval(circlePos.x + circleMovement.x, radius)
+								.getOverlap(Interval (rectPos.x, (size.x / 2))).getLength();
+		float overlapNoMovementY = Interval(circlePos.y, radius)
+								.getOverlap(Interval (rectPos.y, (size.y / 2))).getLength();
+		float overlapMovementY = Interval(circlePos.y + circleMovement.y, radius)
+								.getOverlap(Interval (rectPos.y, (size.y / 2))).getLength();
+		return 	(((overlapNoMovementX < overlapMovementX) && (overlapNoMovementY > 0)) ||
+				((overlapNoMovementY < overlapMovementY) && (overlapNoMovementX > 0)));
+	}
+	// Rectangles can't move and thus not collide.
+	return false;
+}
+
 /**
  * Deletes any sprites which return true for getDelete().
  */
@@ -77,3 +161,44 @@ World::draw(sf::RenderTarget& target, sf::RenderStates states) const {
 	}
 }
 
+/**
+ * Creates an interval from a center point and a radius. The interval
+ * ranges from center - radius to center + radius.
+ */
+World::Interval::Interval(float center, float radius) :
+		start(center - radius),
+		end(center + radius) {
+}
+
+/**
+ * Returns the overlap between two intervals, e.g. the overlap between
+ * intervals (1,3) and (2,4) is (2,3).
+ */
+World::Interval
+World::Interval::getOverlap(Interval other) const {
+	if ((start == other.start) && (end == other.end)) {
+		return *this;
+	}
+	Interval smaller = *this;
+	Interval bigger = other;
+	if (smaller.start > bigger.start) {
+		std::swap(smaller, bigger);
+	}
+	Interval iv(0, 0);
+	if (bigger.start < smaller.end) {
+		iv.start = bigger.start;
+		iv.end = smaller.end;
+	}
+	else {
+		iv.start = iv.end = 0.0f;
+	}
+	return iv;
+}
+
+/**
+ * Returns the length of the interval (distance between start and end).
+ */
+float
+World::Interval::getLength() {
+	return end - start;
+}
diff --git a/source/World.h b/source/World.h
index 243ec1a..91bac8d 100755
--- a/source/World.h
+++ b/source/World.h
@@ -34,7 +34,17 @@ public:
 
 // Private functions.
 private:
+	class Interval {
+	public:
+		float start;
+		float end;
+		Interval(float center, float radius);
+		Interval getOverlap(Interval other) const;
+		float getLength();
+	};
+
     void draw(sf::RenderTarget& target, sf::RenderStates states) const;
+    bool testCollision(std::shared_ptr<Sprite> spriteA, std::shared_ptr<Sprite> spriteB, int elapsed) const;
 
 // Private variables.
 private: