Both observations and deeply theoretical considerations indicate that general relativity, our elegant standard model of gravity, requires modifications at high curvatures scales. Candidate theories of quantum gravity, in their low-energy limit, typically predict couplings to additional fields or extensions that involve higher curvature terms.
At the same time, the breakthrough discovery of gravitational waves has opened a new channel to probe gravity in its most extreme, nonlinear regime. Modelling the expected gravitational radiation in these extensions of GR enables us to search for -- or place novel observational bounds on -- deviations from our standard model. In this talk I will give an overview of the recent progress on simulating binary collisions in these situations.