Gravitational wave (GW) provides a powerful method to test the fundamental properties of gravity in strong-gravitational fields. In this talk, I will introduce the the methods and status of testing gravity with GW observations, including the model-dependent method and the model-independent method. In particular, I will introduce the characters, (including the polarization, amplitude, phase, speed) of GWs in various theories of gravity (General Relativity, Brans-Dicke gravity, General screened modified gravity, Einstein-aether gravity, General parity-violating gravity, etc.), and how to utilize these characters to test the fundamental properties of gravity.
