About half of the nuclei heavier than iron observed in nature are produced by the
so-called rapid neutron capture process, or r-process, of nucleosynthesis. The
identification of the astrophysics site and the specific conditions in which the
r-process takes place remains, however, one of the still-unsolved mysteries of modern
astrophysics. Another underlying difficulty associated with our understanding of the
r-process concerns the uncertainties in the predictions of nuclear properties for the few
thousands exotic neutron-rich nuclei involved in the r-process and for which essentially
no experimental data exist.
The present contribution emphasizes some important future
challenges faced by nuclear physics in this problem, particularly in the determination
of the radiative neutron capture rates by exotic nuclei close to the neutron drip line
and the fission probabilities of heavy neutron-rich nuclei. These quantities are
particularly relevant to determine the composition of the matter resulting from the
r-process. Both the astrophysics and the nuclear physics difficulties
are critically reviewed with a special attention paid to the r-process taking place
during the decompression of neutron star matter.