  If one assumes the validity of conventional quantum field theory in the
vicinity of the horizon of a black hole, one does not find a quantum mechanical
description of the entire black hole that even remotely resembles that of
conventional forms of matter; in contrast with matter made out of ordinary
particles one finds that, even if embedded in a finite volume, a black hole
would be predicted to have a strictly continuous spectrum.
  Dissatisfied with such a result, which indeed hinges on assumptions
concerning the horizon that may well be wrong, various investigators have now
tried to formulate alternative approaches to the problem of ``quantizing" the
black hole. We here review the approach based on the assumption of quantum
mechanical purity and unitarity as a starting point, as has been advocated by
the present author for some time, concentrating on the physics of the states
that should live on a black hole horizon. The approach is shown to be powerful
in not only producing promising models for the quantum black hole, but also new
insights concerning the dynamics of physical degrees of freedom in ordinary
flat space-time.
