With the advent of gravitational wave astronomy we are now in a perfect position to confront the multitude of beyond-GR theories, typically invoked to connect to quantum gravity paradigms, with actual observations in the strong-field regime of gravity. A necessary ingredient to do so, either via theory-specific tests or to inform parametrized approaches, are theoretical predictions of the (gravitational) radiation emitted by compact binaries in extensions of general relativity. In this talk I will present recent results on modelling black hole binaries in scalar Gauss-Bonnet gravity, a well-motivated theory that involves higher-curvature corrections to Einstein's equations. As black holes in this theory can acquire scalar hair or spontaneously scalarize, binaries thereof yield new phenomena such as additional scalar radiation, dephasing of the gravitational wave signal and, possibly most excitingly, dynamical de-scalarization.