### Abstract

The black hole information loss problem has been the focus of much debate for the past thirty years. I will review the path integral approach to the problem: how it can be seen that black holes evaporate (Hartle-Hawking) thus apparently destroying information and how the sum over (Euclidean) space-time topologies may lead to a recovery of the information (Maldacena, Hawking). I will also point out why this may not be the end of the story (Barbon-Rabinovici) and, time permitting, mention a related holographic black hole non-formation argument to solve the problem which I am working on with Germani and Ishibashi.