Colliding Black Holes and Gravitational Waves

This article presents a summary of numerical simulations of black-hole spacetimes in the framework of general relativity. The first part deals with the 3+1 decomposition of generic spacetimes as well as the Einstein equations which forms the basis or most work in numerical relativity. Technical aspects of the resulting numerical evolutions and the diagnostics of the resulting spacetimes are discussed. The second part presents an overview of the history of numerical simulations of black-hole spacetimes. Finally, we summarize results derived from numerical blackhole simulations obtained after the breakthrough in 2005. The relevance of these results in the context of astrophysics, gravitational wave physics, and fundamental physics is discussed.