In most branches of fundamental physics, if one knows the initial state of a system exactly then one can predict its future state exactly. But in General Relativity this statement appears to be violated by charged or rotating black holes. These possess inner horizons beyond which spacetime is not predictable from initial data describing the universe before the black hole formed. The strong cosmic censorship conjecture asserts that this behaviour is always unstable, and thereby rescues determinism. I will review the status of this conjecture and mention recent work pointing to some possible counterexamples.