Modelling inpiraling binaries of compact objects by means of the post-Newtonian approximation: status and challenges

The post-Newtonian approximation is a versatile perturbative scheme suitable to describe isolated systems in the small velocity, weak field regime of general relativity. It is being used extensively to model the dynamics of inspiraling binaries of compact objects, which are known to be excellent sources for gravitational-wave detectors. In this talk, I shall present a selection of results about those systems that have been obtained over the last few years within the post-Newtonian approach. As one may have a priori expected, the most relevant observable quantities have been computed with higher and higher accuracy; but, in addition, quite interestingly, more finite-size effects have been incorporated to the equations of evolution and the gravitational waveform.