Abstract: To be observed and analyzed by the gravitational wave detectors LIGO and VIRGO, inspiralling compact binaries require high-accuracy templates predicted by general relativity theory. These very relativistic systems (with orbital velocities of the order of half the speed of light in the last rotations) are ideally suited for application of a high-order post-Newtonian (PN) gravitational wave generation formalism. In this seminar we shall review the formalism for general PN sources, and its application to compact binary systems. We shall present the currently known templates of inspiralling compact binaries which reach the 3.5PN precision.