  Recent breakthroughs in the field of numerical relativity have led to
dramatic progress in understanding the predictions of General Relativity for
the dynamical interactions of two black holes in the regime of very strong
gravitational fields. Such black-hole binaries are important astrophysical
systems and are a key target of current and developing gravitational-wave
detectors. The waveform signature of strong gravitational radiation emitted as
the black holes fall together and merge provides a clear observable record of
the process. After decades of slow progress, these mergers and the
gravitational-wave signals they generate can now be routinely calculated using
the methods of numerical relativity. We review recent advances in understanding
the predicted physics of events and the consequent radiation, and discuss some
of the impacts this new knowledge is having in various areas of astrophysics.
