Gravitational waves are ripples in spacetime generated by the acceleration of astrophysical objects; a direct consequence of general relativity, they were first directly observed in 2015. Here, I review the first 5 years of gravitational-wave detections. More than 50 gravitational-wave events have been found, emitted by pairs of merging compact objects such as neutron stars and black holes. These signals yield insights into the formation of compact objects and their progenitor stars, enable stringent tests of general relativity, and constrain the behavior of matter at densities higher than that of an atomic nucleus. Mergers that emit both gravitational and electromagnetic waves probe the formation of short gamma-ray bursts and the nucleosynthesis of heavy elements, and they measure the local expansion rate of the Universe.