The Einstein equations can be seen as a system of quasi-linear wave equations, up to the diffeomorphism invariance of their solutions. When posed as an initial value problem, their geometric nature can lead to the failure of global uniqueness of solutions without any loss of regularity. This phenomenon, which occurs in notable black hole interiors, is loosely identified with a breakdown of “Laplacian” determinism. The strong cosmic censorship conjecture (SCCC) posits that determinism is safe in the realm of classical general relativity: geometric extensions beyond the domain of dependence of complete initial hypersurfaces should be unstable in a suitable sense. In this talk, I will discuss modern PDE formulations of the SCCC. I will also present some recent results for a non-linear toy model describing spherically symmetric charged black holes with a positive cosmological constant, for which the $H^1$ formulation of the SCCC is actually expected to fail under appropriate conditions.