  We discuss replica symmetry breaking (RSB) in spin glasses. We update work in
this area, from both the analytical and numerical points of view. We give
particular attention to the difficulties stressed by Newman and Stein
concerning the problem of constructing pure states in spin glass systems. We
mainly discuss what happens in finite-dimensional, realistic spin glasses.
Together with a detailed review of some of the most important features, facts,
data, and phenomena, we present some new theoretical ideas and numerical
results. We discuss among others the basic idea of the RSB theory, correlation
functions, interfaces, overlaps, pure states, random field, and the dynamical
approach. We present new numerical results for the behaviors of coupled
replicas and about the numerical verification of sum rules, and we review some
of the available numerical results that we consider of larger importance (for
example, the determination of the phase transition point, the correlation
functions, the window overlaps, and the dynamical behavior of the system).
