  The astrophysical rapid neutron capture process or `$r$ process' of
nucleosynthesis is believed to be responsible for the production of
approximately half the heavy element abundances found in nature. This
multifaceted problem remains one of the greatest open challenges in all of
physics. Knowledge of nuclear physics properties such as masses, $\beta$-decay
and neutron capture rates, as well as $\beta$-delayed neutron emission
probabilities are critical inputs that go into calculations of $r$-process
nucleosynthesis. While properties of nuclei near stability have been
established, much still remains unknown regarding neutron-rich nuclei far from
stability that may participate in the $r$ process. Sensitivity studies gauge
the astrophysical response of a change in nuclear physics input(s) which allows
for the isolation of the most important nuclear properties that shape the final
abundances observed in nature. This review summarizes the extent of recent
sensitivity studies and highlights how these studies play a key role in
facilitating new insight into the $r$ process. The development of these tools
promotes a focused effort for state-of-the-art measurements, motivates
construction of new facilities and will ultimately move the community towards
addressing the grand challenge of `How were the elements from iron to uranium
made?'.
