  The mechanisms which give rise to Hawking radiation are revealed by analyzing
in detail pair production in the presence of horizons. In preparation for the
black hole problem, three preparatory problems are dwelt with at length: pair
production in an external electric field, thermalization of a uniformly
accelerated detector and accelerated mirrors. In the light of these examples,
the black hole evaporation problem is then presented.
  The leitmotif is the singular behavior of modes on the horizon which gives
rise to a steady rate of production. Special emphasis is put on how each
produced particle contributes to the mean albeit arising from a particular
vacuum fluctuation. It is the mean which drives the semiclassical back
reaction. This aspect is analyzed in more detail than heretofore and in
particular its drawbacks are emphasized. It is the semiclassical theory which
gives rise to Hawking's famous equation for the loss of mass of the black hole
due to evaporation $dM/dt \simeq -1/M^2$. Black hole thermodynamics is derived
from the evaporation process whereupon the reservoir character of the black
hole is manifest. The relation to the thermodynamics of the eternal black hole
through the Hartle--Hawking vacuum and the Killing identity are displayed.
  It is through the analysis of the fluctuations of the field configurations
which give rise to a particular Hawking photon that the dubious character of
the semiclassical theory is manifest. The present frontier of research revolves
around this problem and is principally concerned with the fact that one calls
upon energy scales that are greater than Planckian and the possibility of a non
unitary evolution as well. These last subjects are presented in qualitative
fashion only, so that this review stops at the threshold of quantum gravity.
