The observation of gravitational wave signals by the two interferometers of the Laser Interferometer Gravitational-Wave Observatory (LIGO), and by the Virgo interferometer, has brought the first direct evidence for the existence of black holes, and has also been the first observation of gravitational waves in the wave-zone. After reviewing the historical path that led to our understanding of gravitational waves and black holes, the colloquium will present the theoretical developments on the motion and gravitational radiation of binary black holes that have been crucial in interpreting the LIGO-Virgo

events as being emitted by the coalescence of two black holes.