Black holes present fundamental conceptual puzzles about the effects of quantum mechanics on gravity. At the same time, there is strong evidence that at a fundamental level, black holes can be seen as examples of highly chaotic quantum many-body systems. The universality that emerges in the dynamics of quantum chaotic systems provides a useful and conceptually controlled approach to understanding black hole physics. Quantities from quantum information theory play a key role in understanding both black holes and chaotic many-body systems systems, as well as the relation between them. In this talk, I will provide concrete examples of this fruitful exchange among the fields of quantum gravity, quantum many-body physics, and quantum information theory in the context of evaporating black holes.