The rapid-neutron capture process (r process) is identified as the producer of about 50% of elements heavier than iron.This process requires an astrophysical environment with an extremely high neutron flux over a short amount of time (∼ seconds), creating very neutron-rich nuclei that are subsequently transformed to stable nuclei via β − decay. In 2017, one site for the r process was confirmed: the advanced LIGO and advanced Virgo detectors observed two neutron stars merging, and immediate follow-up measurements of the electromagnetic transients demonstrated an "afterglow" over a broad range of frequencies fully consistent with the expected signal of an r process taking place. Although neutronstar mergers are now known to be r-process element factories, contributions from other sites are still possible, and a comprehensive understanding and description of the r process is still lacking. One key ingredient to large-scale r-process reaction networks is radiative neutron-capture (n, γ) rates, for which there exist virtually no data for extremely neutronrich nuclei involved in the r process. Due to the current status of nuclear-reaction theory and our poor understanding of basic nuclear properties such as level densities and average γ-decay strengths, theoretically estimated (n, γ) rates may vary by orders of magnitude and represent a major source of uncertainty in any nuclear-reaction network calculation of rprocess abundances. In this review, we discuss new approaches to provide information on neutron-capture cross sections and reaction rates relevant to the r process. In particular, we focus on indirect, experimental techniques to measure radiative neutron-capture rates. While direct measurements are not available at present, but could possibly be realized in the future, the indirect approaches present a first step towards constraining neutron-capture rates of importance to the r process.