  Thanks to the new generation of gravitational wave detectors LIGO and VIRGO,
the theory of general relativity will face new and important confrontations to
observational data with unprecedented precision. Indeed the detection and
analysis of the gravitational waves from compact binary star systems requires
beforehand a very precise solution of the two-body problem within general
relativity. The approximation currently used to solve this problem is the
post-Newtonian one, and must be pushed to high order in order to describe with
sufficient accuracy (given the sensitivity of the detectors) the inspiral phase
of compact bodies, which immediately precedes their final merger. The resulting
post-Newtonian ``templates'' are currently known to 3.5PN order, and are used
for searching and deciphering the gravitational wave signals in VIRGO and LIGO.
