Underground hydrogen storage (UHS) in salt caverns is a sustainable energy solution to reduce global warming. Salt rocks provide an exceptional insulator to store natural hydrogen, as they have low porosity and permeability. Nevertheless, the salt creeping nature and hydrogen-induced impact on the operational infrastructure threaten the integrity of the injection/production wells. Furthermore, the scarcity of global UHS initiatives indicates that investigations on well integrity remain insufficient. This study strives to profoundly detect the research gap and imperative considerations for well integrity preservation in UHS projects. The research integrates the salt critical characteristics, the geomechanical and geochemical risks, and the necessary measurements to maintain well integrity. The casing mechanical failure was found as the most challenging threat. Furthermore, the corrosive and erosive effects of hydrogen atoms on cement and casing may critically put the well integrity at risk. The research also indicated that the simultaneous impact of temperature on the salt creep behavior and hydrogen-induced corrosion is an unexplored area that has scope for further research. This inclusive research is an up-to-date source for analysis of the previous advancements, current shortcomings, and future requirements to preserve well integrity in UHS initiatives implemented within salt caverns.