  The last decade has witnessed both quantitative and qualitative progresses in
Shell Model studies, which have resulted in remarkable gains in our
understanding of the structure of the nucleus. Indeed, it is now possible to
diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using
the Lanczos tridiagonal construction, whose formal and numerical aspects we
will analyze. Besides, many new approximation methods have been developed in
order to overcome the dimensionality limitations. Furthermore, new effective
nucleon-nucleon interactions have been constructed that contain both two and
three-body contributions. The former are derived from realistic potentials
(i.e., consistent with two nucleon data). The latter incorporate the pure
monopole terms necessary to correct the bad saturation and shell-formation
properties of the realistic two-body forces. This combination appears to solve
a number of hitherto puzzling problems. In the present review we will
concentrate on those results which illustrate the global features of the
approach: the universality of the effective interaction and the capacity of the
Shell Model to describe simultaneously all the manifestations of the nuclear
dynamics either of single particle or collective nature. We will also treat in
some detail the problems associated with rotational motion, the origin of
quenching of the Gamow Teller transitions, the double beta-decays, the effect
of isospin non conserving nuclear forces, and the specificities of the very
neutron rich nuclei. Many other calculations--that appear to have ``merely''
spectroscopic interest--are touched upon briefly, although we are fully aware
that much of the credibility of the Shell Model rests on them.
