The class of spacetimes with event horizons contain some of the most fascinating solutions to the equations of general relativity. Over the past few years, numerical simulations have begun to reveal many dynamical, strong-field solutions not amenable to exact analytical or perturbative treatments. In this talk, I will describe 3 such scenarios. First, the inspiral and merger of two black holes, which is thought to occur frequently in the universe. Such events are powerful emitters of gravitational waves, and a concerted world-wide effort is currently underway to observe them. Second, I will discuss the ultra-relativistic collision of two solitons. Arguments suggest that at sufficiently high velocities gravity dominates the interaction, causing a black hole to form. These arguments underlie claims that the Large Hadron Collider, or cosmic ray collisions with the Earth, will produce black holes in speculative large extra dimension scenarios. Finally, I will show results elucidating the fate of a black string in 5 dimensions, subject to the Gregory-Laflamme instability. Rather remarkably, the event horizon exhibits dynamics akin to a low viscosity fluid stream suffering the Raleigh-Plateau "beading" instability. In the gravitational process arbitrarily large spacetime curvatures are revealed to an external observer, culminating in naked singularities.