Testing the predictions of general relativity in the dynamical strong-field regime, in particular
black holes and their dynamics, has only recently become possible with LIGO/Virgo observations of black hole mergers. I will review some of the tests that have been performed to date. However, one obstacle to extracting the most stringent constraints possible from the data are the lack of predictions of what the coalescence phase of black hole mergers should like in gravitational wave emission within modified gravity theories (or theories that claim exotic alternatives to black holes). To make things worse, there are doubts to how well-posed many modified gravity theories, than in principle might offer interesting merger dynamics, are. One such theory is Einstein-dilaton-Gauss-Bonnet (EdGB) gravity. I will describe early results beginning to address the well-posedness of EdGB gravity within the dynamical strong-field regime. We restrict attention to gravitational collapse in spherical symmetry, and show for sufficiently strong coupling EdGB gravity is not well-posed from the perspective of the Cauchy initial value problem.