Space warfare is when combat takes place in outer space. For the purposes of this article it will refer to battles where the targets themselves are in space.
History
The history of space warfare goes back to the 1960s when the Soviet Union began the Almaz project, a project designed to give them the ability to do on-orbit inspections of satellites and destroy them if needed. Similar planning in the United States took the form of the Blue Gemini project (comprised of modified Gemini capsules that would be able to deploy weapons and perform surveillance).
Through the 1970s, the Soviet Union continued their project and even test fired a cannon to test space station defense.
Space warfare strongly influenced the final design of the US Space Shuttle. The distinctive delta wing shape was needed if the shuttle were to launch a military payload towards the Soviet Union and perform an immediate de-orbit after one rotation to avoid being shot down.
Both the Soviets and the US developed anti-satellite weaponry designed to shoot down satellites. None of these systems are active today.
Theoretical Space Weaponry
In the late 1970's and throught the 1980's the soviet union and the US theorised, designed and in some cases even tested an astonishing variety of bizarre and exotic weaponry designed for warfare in outer space. Space Warfare was seen primarily as an extension of Nuclear Warfare , and thus theoretical systems were based around the destruction and/or defense of ground and sea-based missiles (The Outer Space Treaty banned the use, testing of or storage of Nuclear weapons outside the Earth's atmosphere). Systems proposed ranged from measures as simple as ground and space-based anti-missiles to railguns, space based lasers, orbital mines and other such futuristic weaponry. If the cold war had continued, then many of these systems could have seen deployment: the US got as far as developing working railguns, and a laser that could destroy missiles at range (though the power requirements of both were phenomenal and the ranges and firing cycles utterly impractical).
The Future
Space warfare of the future may eventually involve humans fighting each other. Many movies have attempted to portray combat in space as an extension of air to air 'dog fighting', but the velocities involved suggest that any actual fighting will be computer driven.