  Largely motivated by the development of highly sensitive gravitational-wave
detectors, our understanding of merging compact binaries and the gravitational
waves they generate has improved dramatically in recent years. Breakthroughs in
numerical relativity now allow us to model the coalescence of two black holes
with no approximations or simplifications. There has also been outstanding
progress in our analytical understanding of binaries. We review these
developments, examining merging binaries using black hole perturbation theory,
post-Newtonian expansions, and direct numerical integration of the field
equations. We summarize these approaches and what they have taught us about
gravitational waves from compact binaries. We place these results in the
context of gravitational-wave generating systems, analyzing the impact
gravitational wave emission has on their sources, as well as what we can learn
about them from direct gravitational-wave measurements.
