  Although we have convincing evidence that a black hole bears an entropy
proportional to its surface (horizon) area, the ``statistical mechanical''
explanation of this entropy remains unknown. Two basic questions in this
connection are: what is the microscopic origin of the entropy, and why does the
law of entropy increase continue to hold when the horizon entropy is included?
After a review of some of the difficulties in answering these questions, I
propose an explanation of the law of entropy increase which comes near to a
proof in the context of the ``semi-classical'' approximation, and which also
provides a proof in full quantum gravity under the assumption that the latter
fulfills certain natural expectations, like the existence of a conserved energy
definable at infinity. This explanation seems to require a fundamental
spacetime discreteness in order for the entropy to be consistently finite, and
I recall briefly some of the ideas for what the discreteness might be. If such
ideas are right, then our knowledge of the horizon entropy will allow us to
``count the atoms of spacetime''.
