Numerical Simulation of Binary Black Holes

The coalescence of binary black hole systems is expected to be an excellent source of gravitational radiation for detectors such as LIGO and LISA. Robust, accurate, and long-term numerical simulations of astrophysically realistic binary black hole systems have yet to be achieved, but tremendous progress towards this goal has been made recently. I will discuss some of the challenges involved, present recent results, and speculate about solutions to some of the remaining problems.