  The study of general two dimensional models of gravity allows to tackle basic
questions of quantum gravity, bypassing important technical complications which
make the treatment in higher dimensions difficult. As the physically important
examples of spherically symmetric Black Holes, together with string inspired
models, belong to this class, valuable knowledge can also be gained for these
systems in the quantum case. In the last decade new insights regarding the
exact quantization of the geometric part of such theories have been obtained.
They allow a systematic quantum field theoretical treatment, also in
interactions with matter, without explicit introduction of a specific classical
background geometry. The present review tries to assemble these results in a
coherent manner, putting them at the same time into the perspective of the
quite large literature on this subject.
