Conformal field theory, (2+1)-dimensional gravity and the BTZ black hole

In three spacetime dimensions, general relativity becomes a topological field theory, whose dynamics can be largely described holographically by a two-dimensional conformal field theory at the 'boundary' of spacetime. I review what is known about this reduction-mainly within the context of pure (2 + 1)dimensional gravity-and discuss its implications for our understanding of the statistical mechanics and quantum mechanics of black holes.