  The post-Newtonian expansion appears to be a relevant tool for predicting the
gravitational waveforms generated by some astrophysical systems such as
binaries. In particular, inspiralling compact binaries are well-modelled by a
system of two point-particles moving on a quasi-circular orbit whose decay by
emission of gravitational radiation is described by a post-Newtonian expansion.
In this paper we summarize the basics of the computation by means of a series
of multipole moments of the exterior field generated by an isolated source in
the post-Newtonian approximation. This computation relies on an ansatz of
matching the exterior multipolar field to the inner field of a slowly-moving
source. The formalism can be applied to point-particles at the price of a
further ansatz, that the infinite self-field of point-particles can be
regularized in a certain way. As it turns out, the concept of point-particle
requires a precise definition in high post-Newtonian approximations of general
relativity.
