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 multiwavelength 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 goal of outlining a path toward resolving the remaining mysteries of the r-process.