The r-process, or the rapid neutron-capture process, of stellar nucleosynthesis is called for to explain the production of the stable (and some long-lived radioactive) neutron-rich nuclides heavier than iron that are observed in stars of various metallicities, as well as in the solar system. A very large amount of nuclear information is necessary in order to model the r-process. This concerns the static characteristics of a large variety of light to heavy nuclei between the valley of stability and the vicinity of the neutron-drip line, as well as their beta-decay branches or their reactivity. The enormously challenging experimental and theoretical task imposed by all these requirements is reviewed, and the state-of-the-art development in the field is presented. Nuclear-physics-based and astrophysics-free r-process models of different levels of sophistication have been constructed over the years. We review their merits and their shortcomings. For long, the core collapse supernova of massive stars has been envisioned as the privileged r-process location. We present a brief summary of the one- or multidimensional spherical or non-spherical explosion simulations available to-date. Their predictions are confronted with the requirements imposed to obtain an r-process. The possibility of r-nuclide synthesis during the decompression of the matter of neutron stars following their merging is also discussed.
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