Astrophysics of Binary Black Holes at the Dawn of Gravitational-Wave Astronomy

Nearly a century after gravitational waves were first predicted by general relativity, gravitational waves were directly observed in September 2014, marking the beginning of the field of gravitational-wave astronomy. These travelling distortions of spacetime came from the collision of two black holes, the corpses of massive stars, over a billion light-years away. In the five years since this initial discovery, we have observed dozens more collisions of these cosmic corpses. In this thesis, I introduce theoretical models and computational methods to use this population of observations to learn how stars interact and explode, and probe the nature of spacetime.