  In this article we review the state of the art on the transport properties of
quantum dot systems connected to superconducting and normal electrodes. The
review is mainly focused on the theoretical achievements although a summary of
the most relevant experimental results is also given. A large part of the
discussion is devoted to the single level Anderson type models generalized to
include superconductivity in the leads, which already contains most of the
interesting physical phenomena. Particular attention is paid to the competition
between pairing and Kondo correlations, the emergence of \pi-junction behavior,
the interplay of Andreev and resonant tunneling, and the important role of
Andreev bound states which characterized the spectral properties of most of
these systems. We give technical details on the several different analytical
and numerical methods which have been developed for describing these
properties. We further discuss the recent theoretical efforts devoted to extend
this analysis to more complex situations like multidot, multilevel or
multiterminal configurations in which novel phenomena is expected to emerge.
These include control of the localized spin states by a Josephson current and
also the possibility of creating entangled electron pairs by means of non-local
Andreev processes.
