Gravitational waves (GWs) are signals that propagate across large distances in the Universe, and thus, they bring information on the history of the Universe. GW sources are at the same time distance indicators and tracers of the matter field. Events generated by binary systems can be divided into bright standard sirens, when followed by electromagnetic transients from which the redshift of the source can be measured, and the more numerous dark standard sirens, when counterparts are not available. In this talk, we will discuss about tests of the cosmological model and of gravity theories using both bright and dark sirens and their combinations with other cosmological probes. I will first present prospects for testing cosmic distance relations with future surveys from the recent work [arXiv:2311.17176]. Then, I will share some ideas of an ongoing project in which we propose the use of angular cross-correlations of dark sirens and galaxies to make a model-independent cosmological test.