The age of gravitational-wave astronomy is now in full swing: For the first time, we gain observational access to the highly dynamical strong-field regime of the gravitational interaction. Constraining potential deviations from General Relativity (GR) requires reliable waveform predictions, not just in GR, but also when higher curvature corrections contribute to the dynamics. I will present an overview of recent progress on
(i) longlived classical time evolution in the presence of ghosts,
(ii) mathematical well-posedness of the initial value problem,
(iii) numerical relativity simulations to obtain full nonlinear waveforms.
In combination, this opens up a feasible pathway to use current and future gravitational-wave observations to constrain effective field theories of gravity.