  We review the current status of heavy quark symmetry and its applications to
weak decays of hadrons containing a single heavy quark. After an introduction
to the underlying physical ideas, we discuss in detail the formalism of the
heavy quark effective theory, including a comprehensive treatment of symmetry
breaking corrections. We then illustrate some nonperturbative approaches, which
aim at a dynamical, QCD-based calculation of the universal form factors of the
effective theory. The main focus is on results obtained using QCD sum rules.
Finally, we perform an essentially model-independent analysis of semileptonic
$B$ meson decays in the context of the heavy quark effective theory.
