  Black hole formation and evaporation is studied in the semiclassical
approximation in simple 1+1-dimensional models, with emphasis on issues related
to Hawking's information paradox. Exact semiclassical solutions are described
and questions of boundary conditions and vacuum stability are discussed. The
validity of the semiclassical approximation has been called into question in
the context of the information puzzle. A different approach, where black hole
evolution is assumed to be unitary, is described. It requires unusual causal
properties and kinematic behavior of matter that may be realized in string
theory. Based on lectures given at the 1994 Trieste Spring School
