Gravitational waves (GWs) offer a unique observational window into the nature of gravity. In particular, the remnant black hole formed after the merger of two compact objects emits GWs with a characteristic spectrum that allows to probe directly the gravitational interactions. This GW emission--known as the ringdown--is typically modelled using linear perturbation theory, which has been shown to work remarkably well. In this talk, I will first argue that gravitational nonlinearities may have a surprisingly small effect on the observed GW ringdown, although they may still be resolvable. I will then show evidence for nonlinearities in the ringdown from black hole numerical simulations. When including these nonlinear effects, GW ringdown models improve their fittings to simulations by up to two orders of magnitude, which suggests the need to be accounted for in future data analyses.