  We review some recent works on the post-Newtonian theory of slowly-moving
(post-Newtonian) sources, and its application to the problems of dynamics and
gravitational radiation from compact binary systems. Our current knowledge is
3PN on the center-of-mass energy and 3.5PN on the gravitational-wave flux of
inspiralling compact binaries. We compute the innermost circular orbit (ICO) of
binary black-hole systems and find a very good agreement with the result of
numerical relativity. We argue that the gravitational dynamics of two bodies of
comparable masses in general relativity does not resemble that of a test
particle on a Schwarzschild background. This leads us to question the validity
of some ``Schwarzschild-like'' templates for binary inspiral which are
constructed from post-Newtonian resummation techniques.
