  These are lecture notes for the 1992 Erice Workshop on Theoretical Physics.
They first present a summary of the paradox of information loss to black holes,
of its proposed resolutions, and of the flaws in the proposed resolutions.
There follows a review of recent attempts to attack this problem, and other
issues in black hole physics, using two-dimensional dilaton gravity theories as
toy models. These toy models contain collapsing black holes and have for the
first time enabled an explicit semiclassical treatment of the backreaction of
the Hawking radiation on the geometry of an evaporating black hole. However, a
complete answer to the information conundrum seems to require physics beyond
the semiclassical approximation. Preliminary attempts to make progress in this
direction, using connections to conformal field theory, are described.
