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This is an exciting time for the study of r-process nucleosynthesis. Recently, a neutron star merger GW170817 was observed in extraordinary detail with gravitational waves and electromagnetic radiation from radio to γ rays. The very red color of the associated kilonova suggests that neutron star mergers are an important r-process site. Astrophysical simulations of neutron star mergers and core collapse supernovae are making rapid progress. Detection of both electron neutrinos and antineutrinos from the next galactic supernova will constrain the composition of neutrino-driven winds and provide unique nucleosynthesis information. Finally, FRIB and other rare-isotope beam facilities will soon have dramatic new capabilities to synthesize many neutron-rich nuclei that are involved in the r-process. The new capabilities can significantly improve our understanding of the r-process and likely resolve one of the main outstanding problems in classical nuclear astrophysics. However, to make best use of the new experimental capabilities and to fully interpret the results, a great deal of infrastructure is needed in many related areas of astronomy, astrophysics, and nuclear theory. We place these experiments in context by discussing astrophysical simulations and observations of r-process sites, observations of stellar abundances, galactic chemical evolution, and nuclear theory for the structure and reactions of very neutron-rich nuclei. This review paper was initiated at a three-week International Collaborations in Nuclear Theory program in June 2016, where we explored promising r-process experiments and discussed their likely impact, and their astronomical, astrophysical, and nuclear theory context. [ABSTRACT FROM AUTHOR]