  Nuclear many-body theory is used to study nuclear matter and finite nuclei at
extreme isospin. In-medium interactions in asymmetric nuclear matter are
obtained from (Dirac-) Brueckner theory. Neutron skin formation in Ni and Sn
isotopes is investigated by relativistic mean-field calculations in DDRH theory
with density dependent meson-nucleon vertices. Applications to light nuclei are
discussed with special emphasis on pairing and core polarization in weakly
bound nuclei. Approaches accounting for continuum coupling in dripline pairing
and core polarization are presented. Calculations for the halo nuclei $^8$B,
$^{11}$Be and $^{19}$C show that shell structures are dissolving when the
driplines are approached. Relativistic breakup data are well described by
eikonal calculations.
