The rapid neutron capture process (r process) is believed to be responsible for about half of the production of the elements heavier than iron and contributes to abundances of some lighter nuclides as well. A universal pattern of r-process element abundances is observed in some metal-poor stars of the Galactic halo. This suggests that a well-regulated combination of astrophysical conditions and nuclear physics conspires to produce such a universal abundance pattern. The search for the astrophysical site for r-process nucleosynthesis has stimulated interdisciplinary research for more than six decades. There is currently much enthusiasm surrounding evidence for r-process nucleosynthesis in binary neutron star mergers in the multi-wavelength follow-up observations of kilonova/gravitational-wave GRB170807A/GW170817. Nevertheless, there remain questions as to the contribution over the history of the Galaxy to the current solar-system r-process abundances from other sites such as neutrino-driven winds or magnetohydrodynamical ejection of material from core-collapse supernovae. In this review we highlight some current issues surrounding the nuclear physics input, astronomical observations, galactic chemical evolution, and theoretical simulations of r-process astrophysical environments with the goal of outlining a path toward resolving the remaining mysteries of the r process.
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