Black Hole Entropy and the Problem of Universality

A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an embarrassment of riches: many different approaches to quantum gravity yield the same entropy, despite counting very different states. This ``universality'' suggests that some underlying feature of the classical theory may control the quantum density of states. I discuss the possibility that this feature is an approximate two-dimensional conformal symmetry near the horizon.