Black holes, which are made solely of warped space-time, are among the most exotic objects in the universe. When two black holes collide, a tremendous amount of energy is emitted in the form of gravitational waves, ripples in space-time itself traveling at the speed of light. Such collisions are not visible with traditional electromagnetic telescopes and need to be observed with gravitational wave detectors like LIGO. Detection of gravitational waves will lead to the most direct test of Einstein's theory of general relativity as well as to a wealth of new astrophysical insights, ranging from the fate of massive stars to the formation of galaxies in the early universe. Computer simulations play an integral role in this endeavor, both to find gravitational waves and to interpret their meaning. This talk attempts to convey a flavor of these topics.