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Gravity is unique among the other forces in that within general relativity we are able to do calculations which, when properly interpreted, give us information about non-perturbative quantum gravity. A classic example is Bekenstein and Hawking's calculation of the entropy of a black hole, and a more recent example is the calculation of the ``Page curve'' for certain evaporating black holes. A common feature of both of these calculations is that they compute entropies without using von Neumann's formula S=-Tr(\rho \log \rho). In this strange situation where we are able to compute entropies without understanding the details of the states for which they are the entropy, quantum information theory is a powerful tool that lets us extract information about those states. In this talk I'll review aspects of these developments, emphasizing in particular the role of quantum extremal surfaces and quantum error correction.