The first observation of gravitational waves (GWs) from the coalescence of a black-hole binary in 2015 heralded the beginning of a new era in experimental gravity. In just 5 years, the detection of GWs has evolved from non-existent to a weekly business and has led to a wealth of results with important implications for fundamental physics, astrophysics and cosmology. In this talk, I will give an overview of the GW events detected so far by LIGO and Virgo and will describe how these can be used to test general relativity as the underlying theory of gravity. I will focus on an array of analysis methods developed exactly for this purpose and will give an update on their latest results on inferring the true nature of gravity. If time allows, I will briefly discuss the potential of probing fundamental physics with future GW detectors, including upgrades of existing instruments, 3rd generation ground-based interferometers and future space-bound detectors.