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About half of the nuclei heavier than iron observed in nature are produced by the socalled 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 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 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. Their impact on the r-abundance distribution resulting from the decompression of neutron star matter is discussed.