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Supermassive black holes at the centers of galaxies power some of the most energetic phenomena in the Universe. Their observations have numerous exciting consequences for our understanding of galactic evolution, black hole demographics, plasma dynamics in strong-field gravity, and general relativity. When they collide, they produce intense bursts of gravitational and electromagnetic energy and launch powerful relativistic jets. Understanding these systems requires solving the highly-nonlinear and highly-coupled field equations of General Relativity and Relativistic Magnethodrodynamics. It is only with the use of sophisticated numerical techniques for simulations, data extraction and visualization, and running on petascale supercomputers of ten to hundreds of thousands of CPUs simultaneously that this problem is tractable. This talk will review some of the new developments in the field of numerical relativity, and relativistic astrophysics that allow us to successfully simulate and visualize the innermost workings of these violent astrophysical phenomena.