Black Holes in General Relativity and Beyond

The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I go through the physics of the different phases of the evolution of black hole binary systems, providing a qualitative physical interpretation of each one of them. I also briefly describe how these phases would be modified if gravitation were described by a theory extending or deforming General Relativity, or if the binary components turned out to be more exotic compact objects than black holes.