  The development of both ground- and space-based gravitational wave detectors
provides new opportunities to observe the radiation from binaries containing
neutron stars and black holes. Numerical simulations in 3-D are essential for
calculating the coalescence waveforms, and comprise some of the most
challenging problems in astrophysics today. This article briefly reviews the
current status of efforts to calculate black hole and neutron star
coalescences, and highlights challenges for the future.
