To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (LISA, etc.), inspiralling compact binaries --- binary star systems composed of neutron stars and/or black holes in their late stage of evolution --- require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion, in Lagrangian and Hamiltonian formalisms, pay attention to the self-field regularizations at work, discuss several notions of innermost circular orbits and make comparisons with numerical gravitational self-force computations. The gravitational waveform and energy flux are obtained with high post-Newtonian precision. Some landmark results are discussed in the case of eccentric compact binaries moving on quasi-elliptical orbits, and on spin-orbit coupling effects in black hole binaries.