Strong cosmic censorship: how singularities restare determinism

It has been known for a long time that classical determinism can break down in the interior of rotating black holes. In 1968 Roger Penrose found a heuristic mechanism that leads to an instability and the subsequent formation of a singularity in the interior of such black holes. It is the formation of such a singularity that is expected to generically restore determinism. This scenario is known as the strong cosmic censorship conjecture. In this talk I will review this conjecture and also present recent progress towards its resolution.