  Physics of nuclei at extreme values of the isospin is at the focus of
present-day nuclear science. Experimentally, thanks to existing and emerging
radioactive-ion-beam facilities, we are on the verge of invading the territory
of extreme N/Z ratios in an unprecedented way. Theoretically, nuclear exotica
represent a formidable challenge for the nuclear many-body theories and their
power to predict nuclear properties far from stability. Going to the limits of
the nuclear binding is also important for an improvement of our description of
normal nuclei from the neighborhood of the beta stability valley. In the
present talk, we review several aspects of the present-day mean-field
theoretical studies of weakly bound nuclei.
