The production of about half of the heavy elements found in nature is assigned to a specific astrophysical nucleosynthesis process: the rapid neutron capture process (r-process). Although this idea has been postulated more than six decades ago, the full understanding faces two types of uncertainties/open questions: (a) The nucleosynthesis path in the nuclear chart runs close to the neutron-drip line, where presently only limited experimental information is available, and one has to rely strongly on theoretical predictions for nuclear properties. (b) While for many years the occurrence of the r-process has been associated with supernovae, more recent studies have cast substantial doubts on this environment. Alternative scenarios include the mergers of neutron stars, neutron-star black hole mergers, but possibly also rare classes of supernovae as well as hypernovae/collapsars with polar jet ejecta and also accretion disk outflows related to the collapse of fast rotating massive stars with high magnetic fields. Stellar r-process abundance observations, have provided insights into, and constraints on the frequency of and conditions in the responsible stellar production sites. One of them, neutron star mergers, was just identified and related to the Gravitational Wave event GW170817. High resolution observations, increasingly more precise due to improved experimental atomic data, have been particularly important in defining the heavy element abundance patterns of the old halo stars, and thus determining the extent, and nature, of the earliest nucleosynthesis in our Galaxy. Combining new results and important breakthroughs in the related nuclear, atomic and astronomical fields of science, this review attempts to provide an answer to the question How Were the Elements from Iron to Uranium Made? (Abridged)
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