The evolution of the binary under gravitational-wave emission, and the resulting gravitational-wave signal, can be predicted fairly accurately using General Relativity, either via analytic approximations, numerical simulations, or combinations of both. The properties of the gravitational-wave signal depend strongly on the properties of the binary system: the spatial position and orientation of the system with respect to us, the masses and orbital angular momenta (spins) of the compact objects, the orbital eccentricity, and the nature of the compact objects. The availability of predictive models of the signal allows us to do very sensitive searches for coalescing compact binaries in data from gravitational-wave detectors like Virgo, LIGO and KAGRA. Once a signal is identified in the data, we can then also use the models to infer the properties of the source. By collecting many such detections and inferences, we can learn how many black holes and neutron stars are in the Universe, what is the distribution of their masses and spins, what is the structure of neutron stars, whether General Relativity correctly describes black holes and neutron stars, and the properties of any electromagnetic or neutrino emission that could possibly be associated with compact binary mergers.