I will discuss two lines of research to test general relativity in the strong-gravity regime with gravitational wave observations of merging black holes. In general relativity, the quasinormal mode spectrum of black hole merger remnants depends only on their mass and spin. To understand the effect of any modified gravity theory on the spectrum, we must either: 1) identify healthy modified theories of gravity, find black hole solutions within these theories and compute their quasinormal spectrum; or 2) solve the equations describing parametrized deviations from general relativity to compute the characteristic quasinormal modes. I will first introduce a general research program concerning black hole solutions in modified theories with nontrivial coupling between a scalar and the Gauss-Bonnet invariant. These theories can give rise to "black hole spontaneous scalarization". I will explain this phenomenon, discuss various models that lead to scalarization, and present recent progress on binary dynamics in these theories. In the second part of the talk I will discuss a parametrized approach where we assume that the background spacetime has spherical symmetry and that the dynamics of the system is perturbatively close to general relativity. Under these assumptions we found general numerical solutions for the quasinormal mode frequencies, even for coupled systems of perturbation equations. I will discuss possible extensions of this approach to the rotating case.