Nickel-based alloys are considered among other candidate materials as engineering barriers of geological repositories due to their excellent corrosion resistance. These alloys possess unique advantages: they may be used in saturated and unsaturated repositories, hosted by practically any rock type, while also compatible with any (or no) backfill, and have minimal impact in other barriers. Alloy-22 (UNS N06022) has been the most studied of this class of alloys for its potential application in the proposed repositories (namely Yucca Mountain, USA). Crevice corrosion is however an important and often unintended degradation process that may limit the waste container lifetime if a nickel-based alloy is selected. Alloy susceptibility to crevice corrosion is influenced by environmental and metallurgical variables. This review gives an account of the current knowledge regarding crevice corrosion of nickel-based alloys as candidate materials for the corrosion-resistant layer of high-level nuclear waste containers. Although there is a significant amount of research supporting the use of nickel-based alloys for this application, the effect of the different variables on crevice corrosion resistance is described. Special focus is given to the current criterion for crevice corrosion occurrence in repository environments, recent works and criticisms. The presently established criterion appears robust for ruling out crevice corrosion in saturated repositories; however, the development of a less conservative criterion for crevice corrosion occurrence is necessary to use these alloys in unsaturated repositories.