  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.
