As the technologies we use as a society have advanced, so have the materials used in these technologies. Some of these materials are exotic and highly specialized, making them particularly vulnerable to supply disruptions and supply disruptions particularly impactful. Such materials are designated as “critical” materials. Their level of criticality can be identified by accounting for a number of factors related to their supply risk and the extent to which a supply disruption would impact business operations or society at large. We highlight current methodologies used to assess materials criticality, how these assessments are used to reduce materials-related risk and to what extent there is room for improvement. Particularly, this paper reviews critical materials designations from the United States Department of Energy, the European Union, and the General Electric Company, and how they have changed over the period from 2008 to 2014. The changes suggest that the factors considered in criticality ratings have different natural time scales, and that criticality changes occur both due to supply-side risk mitigation as well as demand-side responses. Response options, whether on the supply or demand side, also span a range of time scales and the interaction between factors with different time scales can play a significant role in the dynamics. To date, many published analyses are snapshots in time. A detailed understanding of how risk profiles evolve remains an open question. The importance and impact of demand-side responses such as recycling, substitution and new technological development are discussed.