  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.
