In the first and second observation run of advanced LIGO and Virgo, gravitational waves from ten binary black hole merger events and one binary neutron star merger event have been detected. The gravitational wave window has offered opportunity for the first time to examine the correctness of general relativity in the strong field regime. In this talk, the speaker will first give a brief overview of the current tests of general relativity with gravitational waves performed by LIGO and Virgo. Several testing methods are applied including model agnostic parameterized tests, gravitational wave dispersion relation tests, inspiral-merger-ringdown consistency tests and so on. In the future more gravitational wave detections are anticipated, about one binary black hole merger per week on average during the third observation run. While the above testing methods can be applied on each event, there is no unique way of combining the results from multiple events. Furthermore, he will introduce a method which correlates the degree of violation of general relativity with other source parameters such as distance and mass, for multiple events. If a violation of general relativity exists, this method can offer us insight about the origin of the beyond-general-relativity effects.
