The celebration of general relativity’s centennial also marked the first-ever observation, by the two ground-based Advanced LIGO interferometers, of gravitational waves emitted during the coalescence of two stellar-mass black holes. This was the first direct detection of gravitational waves, but also the first direct evidence for the existence of black holes. This discovery was made possible not only by the exquisite sensitivity of the detectors, but also by an accurate modelling of the orbital dynamics and gravitational-wave emission of black hole binaries. These can be investigated using a variety of approximation schemes and numerical methods in general relativity : the post-Newtonian formalism, black hole perturbation theory, numerical relativity simulations, and the effective one-body model. I will give an introductory overview of each of these analytical and numerical techniques, emphasizing the various interplay between them.