The detection of gravitational waves (GWs) of astrophysical origin provides an exciting discovery and opens a new observational window to test gravitational theories. In this talk, I will first explain how GWs can provide us with important information about gravity at cosmological scales and I will then discuss some important implications of the recent measurement of the speed of GW’s for large classes of gravitational theories beyond General Relativity at the level of large-scale structure of the Universe. Finally, I will
discuss some recent constraints from stellar-structure tests.