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. Although 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.
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