A revolution has taken place over the last two years in our ability to solve Einstein's equations numerically for black hole spacetimes. Several research groups now routinely produce stable and accurate simulations of binary black hole systems. These systems are strong sources of gravitational waves, emitted as the black holes spiral together and ultimately merge into a single hole; and they are among the most likely sources for LIGO. This talk will describe some of the breakthroughs in our understanding of Einstein's equations and some of the interesting numerical techniques that made this revolution possible. Some initial results of these simulations having interesting physical and astrophysical consequences will also be discussed.