Jacob Crow through his dream to create "genetic superiors to the human race" during the Machine Wars of which Crow himself started. Eventually in order to obtain his goal for eternal life - the true meaning of the Timesplitters existence - he turned himself into his own creation; A Timesplitter. As of writing, there are currently five different Timesplitters to have been shown, however they all vary in appearance; as of yet, not actual explanation has been given to their differing appearances game to game. Contrary to the name, Drone Splitters cannot technically be classed as part of the Timesplitters race due to the fact that they are part of another. They were once enslaved by the Timesplitters and furthermore controlled by spinal implants.
During Timesplitters 2, a group of rouge Timesplitters managed to take control of a space station, with their Time Crystals securely in place and managing to keep their Time Portal open. However upon the arrival of Sergeant Cortez and Corporal Hart, the Timesplitters fled through fear of them stealing the time crystals and continued moving through time so to make them harder to find, or ultimately, kill.
Thus during the events of Timesplitters Future Perfect, a group of Berserker Splitters led an army to attack a rebel base in an attempt to prevent Sergeant Cortez from gaining hold of the Time Crystals. However the mother ship was eventually shot down by Cortez in an attempt to save his past self and to secondly stop any more Berserker Splitters from advancing.
 Known Timesplitters
TimeSplitter War Phase 1
The Machine Wars
Mox Civil War
TimeSplitters' Natural Existence