Résumé : 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, for which essentially no experimental data exist.The present paper emphasizes some important future challenges faced by nuclear physics in this problem, particularly in the determination of the nuclear structure properties of exotic neutron-rich nuclei as well as their radiative neutron capture rates and their fission probabilities. 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 special attention paid to the r-process taking place during the decompression of neutron star matter following the merging of two neutron stars.