Analysis of data from the Earth-based gravitational-wave detector LIGO is ongoing while the instrument is being upgraded. The space-based detector LISA, expected to fly within the next decade, will observe massive black holes out to large redshifts, allowing us to study their mass and spin evolution, to check whether they have the properties predicted by Einstein's general relativity, and to set bounds on alternative theories of gravity. I will review the status of our numerical and analytical understanding of gravitational-wave sources, and I will argue that recent theoretical results are already interesting for astrophysics and fundamental physics. Numerical calculations of the recoil velocities and spins resulting from black hole mergers shed light on hierarchical galaxy formation scenarios and on the cosmological evolution of black hole spins. Simulations of ultrarelativistic black hole collisions are improving our understanding of strong-field gravity, and may be relevant for estimates of the energy loss if mini-black hole production occurs at the Large Hedron Collider.