Quasi-normal modes and gravitational wave astronomy

We review the main results obtained in the literature on quasi-normal modes (QNM) of compact stars and black holes, in the light of recent exciting developments of gravitational wave (GW) detectors. QNMs are a fundamental feature of the gravitational signal emitted by compact objects in many astrophysical processes; we will show that their eigenfrequencies encode interesting information on the nature and on the inner structure of the emitting source and we will discuss whether we are ready for a GW asteroseismology.