The ringdown of black holes provides a unique probe of black hole spacetimes and the theory of gravity which governs their perturbations. We will briefly review black hole ringdown and "black hole spectroscopy" using gravitational wave observations. We will then discuss how ringdown frequencies can be predicted in modified theories of gravity, focusing on generic approaches with potential applications within an EFT framework. Finally, we will comment on the related problem of extreme mass ratio inspirals and describe some directions for future research.