All black holes in the Universe are believed to be rotating. This poses interesting questions, since rotating black hole solutions of Einstein’s equations of General Relativity possess a so-called Cauchy horizon in their interior, which threatens the predictability of Einstein’s theory. However, these exact solutions may not model sufficiently accurately black holes in Nature, which have classical matter in their neighbourhood and, furthermore, are inevitably surrounded by a quantum vacuum (which is responsible for Hawking radiation). On the classical side, it has been found that the Cauchy horizons of some black holes become irregular under classical field perturbations whereas the Cauchy horizons of other black holes (e.g., in a Universe with a positive cosmological constant) seem to remain regular. On the quantum side, effects on Cauchy horizons due to quantum fields are believed to be generally stronger than those due to classical fields. In this talk, we will review some results on the linear stability of Cauchy horizons of black holes and we will present recent results on semiclassical effects due to a quantum field on the Cauchy horizon of a rotating (Kerr) black hole. In particular, we will show that the (renormalized) fluxes from a quantum scalar field generically diverge on the Cauchy horizon of a Kerr black hole that is evaporating via the emission of Hawking radiation.