  The precise knowledge of the gravitational phase evolution of compact
binaries is crucial to the data analysis for gravitational waves. Until
recently, it was known analytically (for non-spinning systems) up to the 3.5
post-Newtonian (PN) order, i.e. up to the $(v/c)^7$ correction beyond the
leading order quadrupole formula. Using a PN-multipolar-post-Minkowskian
algorithm, we have pushed the accuracy to the next 4PN level. This derivation
involved challenging technical issues, due to the appearance of non-physical
divergences, which have to be properly regularized, as well as effects of
non-linear multipole interactions.
