Gravitational waves emitted by the compact binary coalescence of binary black holes, neutron star-black holes, and neutron stars, are examples of standard sirens, capable of completely bypassing the cosmic distance scale ladder that hinders local electromagnetic distance measurements. With additional information about their redshift, standard sirens can be used to constrain cosmological parameters. In this talk, I will review the cosmological constraints obtained by the LIGO-Virgo-KAGRA collaboration during the first three (O1-O3) observing runs, and discuss cosmological forecasts with the Extreme Mass-Ratio Inspirals observed by the future space-borne gravitational wave detector LISA.