  Inspiralling compact binaries are ideally suited for application of a
high-order post-Newtonian (PN) gravitational wave generation formalism. To be
observed by the LIGO and VIRGO detectors, these very relativistic systems (with
orbital velocities of the order of 0.5c in the last rotations) require
high-accuracy templates predicted by general relativity theory. Recent
calculations of the motion and gravitational radiation of compact binaries at
the 3PN approximation using the Hadamard self-field regularization have left
undetermined a few dimensionless coefficients called ambiguity parameters. In
this article we review the application of dimensional self-field
regularization, within Einstein's classical general relativity formulated in D
space-time dimensions, which finally succeeded in clearing up the problem, by
uniquely fixing the values of all the ambiguity parameters.
