  We review the dynamical mean-field theory of strongly correlated fermion
systems which is based on a mapping of lattice models onto quantum impurity
models subject to a self-consistency condition. This mapping is exact in the
limit of large lattice coordination (or infinite spatial dimensions). This
method can be used for the determination of phase diagrams and the calculation
of thermodynamic properties, one-particle Green's functions, and response
functions, using analytic and numerical techniques which are described. We
review the recent progress in understanding the Hubbard model and the Mott
metal-insulator transition within this approach, including some comparison to
experiments on three-dimensional transition-metal oxides. Some applications of
this method to other models are also reviewed. The present limitations of the
approach, and possible extensions of the formalism are finally discussed.
Computer programs for the numerical implementation of this method are provided
with this article.
