The heaviest elements - such as uranium and thorium - found on Earth and in the solar system likely owe their origins to an extreme and mysterious astrophysical process: the rapid neutron capture (r-)process of nucleosynthesis. In the past decade there have been several key breakthroughs, including the groundbreaking gravitational wave event GW170817, that suggest neutron star mergers are a likely site for production of r-process species. Still, the extent of the element synthesis in this environment and the role of neutron star mergers in contributing to the galactic tally of r-process elements have yet to be clarified. One key reason is that interpreting clues from r-process observables such as light curves, abundance patterns, and isotopic ratios currently suffers from large uncertainties due in part to the unknown nuclear physics of the thousands of unstable species which participate in the r process. Here we discuss quantifications of these uncertainties as well as what can be learned from specific observables once nuclear uncertainties are reduced. We further speculate on how r-process observables will eventually be used to probe nuclear physics questions entirely inaccessible to terrestrial experiments.