Major astrophysical applications involve a huge number of exotic nuclei. An important effort has been devoted during the last decades to the measurements of the masses and &bgr;‐decay rates of very neutron‐rich nuclei at RIB facilities. However, most of them cannot be synthesised in terrestrial laboratories and only theoretical predictions can fill the gap. We concentrate mainly on the &bgr;‐decay rates needed for the stellar r‐process modeling and for performing the RIB experiments. The continuum QRPA approach based on the self‐consistent ground state description in the framework of the density functional theory is briefly described. The model for the large‐scale calculations of total &bgr;‐decay half‐lives accounts for the Gamow‐Teller and first‐forbidden transitions. Due to the shell configuration effect, the first‐forbidden decays have a strong impact on the total half‐lives of the r‐process relevant nuclei at N=126, Z=60–70. The performance of existing global models for the nuclides near the r‐process paths at N=126 is critically analyzed and confronted with the recent RIB experiments in the region “east” of208Pb . The possible role of neutrino nucleosynthesis is exemplified by the production of rare isotope138La via the neutrino process. © 2004 American Institute of Physics