  The merger of two black holes is one of the most extraordinary events in the
natural world. Made of pure gravity, the holes combine to form a single hole,
emitting a strong burst of gravitational radiation. Ground-based detectors are
currently searching for such bursts from holes formed in the evolution of
binary stars, and indeed the very first gravitational wave event detected may
well be a black-hole merger. The space-based LISA detector is being designed to
search for such bursts from merging massive black holes in the centers of
galaxies, events that would emit many thousands of solar masses of pure
gravitational wave energy over a period of only a few minutes. To assist
gravitational wave astronomers in their searches, and to be in a position to
understand the details of what they see, numerical relativists are performing
supercomputer simulations of these events. I review here the state of the art
of these simulations, what we have learned from them so far, and what
challenges remain before we have a full prediction of the waveforms to be
expected from these events.
