Abstract Major astrophysical applications involve a huge number of exotic nuclei. Their beta-decay properties play a crucial role in stellar explosive events. An important effort has been developed in last decades to measure the masses and β -decay properties of very neutron-rich nuclei at radioactive nuclear beam facilities. However, most of them cannot be synthesized in terrestrial laboratories and only theoretical predictions can fill the gap. We will concentrate mainly on the β -decay rates needed for stellar r-process modeling and for performing the RNB experiments. An overview of the microscopic approaches to the β -decay strength function is given. The continuum QRPA approach based on the self-consistent ground state description in the framework of the density functional theory is outlined. For the first time, a systematic study of the total β -decay half-lives and delayed neutron emission probabilities takes into account the Gamow–Teller and first-forbidden transitions. Due to the shell configuration effects, the first-forbidden decays have a strong impact on the β -decay characteristics of the r-process relevant nuclei at Z ≈ 28 , N > 50 ; Z ⩾ 50 , N > 82 and Z = 60 – 70 , N ≈ 126 . Suppression of the delayed neutron emission probability is found in nuclei with the neutron excess bigger than one major shell. The effect originates from the high-energy first-forbidden transitions to the states outside the ( Q β − B n ) -window in the daughter nuclei. The performance of existing global models for the nuclides near the r-process paths is critically analyzed and confronted with the recent RIB experiments in the regions of 78 Ni, 132 Sn and “east” of 208 Pb.