Hawking famously discovered a tension between semiclassical gravity and the unitary evolution of quantum mechanics when black holes evaporate. I’ll describe a semiclassical calculation that nonetheless reproduces signatures of unitarity, namely the “Page curve” of entropy evolution and the Hayden-Preskill protocol. The new input, coming from recent advances in AdS/CFT, involves a “quantum extremal surface”, a stationary surface for Bekenstein’s generalised entropy. The result implicitly makes use of “Euclidean wormholes”, topologies which connect distant regions of spacetime. I will explore the implications for the information paradox, the semiclassical gravity path integral, and quantum gravity more generally.