  The advent of long-term stability in numerical relativity has yielded a
windfall of answers to long-standing questions regarding the dynamics of
space-time, matter, and electromagnetic fields in the strong-field regime of
black-hole binary mergers. In this review, we will briefly summarize the
methodology currently applied to these problems, emphasizing the most recent
advancements. We will discuss recent results of astrophysical relevance, and
present some novel interpretation. Though we primarily present a review, we
also present a simple analytical model for the time-dependent Poynting flux
from two orbiting black holes immersed in a magnetic field, which compares
favorably with recent numerical results. Finally, we will discuss recent
advancements in our theoretical understanding of merger dynamics and
gravitational waveforms that have resulted from interpreting the ever-growing
body of numerical relativity results.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies;High Energy Astrophysical Phenomena