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In recent literature, the concept of criticality aspires to provide a multifaceted risk assessment of resource supply shortage. However, most existing methodologies for the criticality assessment of raw materials are restricted to a fixed temporal and spatial reference system. They provide a snapshot in time of the equilibrium between supply and demand/economic importance and do not account for temporal changes of their indicators. The static character of criticality assessments limits the use of criticality methodologies to short-term policy making of raw materials. In the current paper, we argue for an enhancement of the criticality framework to account for three key dynamic characteristics, namely changes of social, technical, and economic features; consideration of the spatial dimension in site-specific assessments; and impact of changing governance frameworks. We illustrate how these issues were addressed in studies outside of the field of criticality and identify the dynamic parameters that influence resource supply and demand based on a review of studies that belong to the general field of resource supply and demand. The parameters are grouped in seven categories: extraction, social, economic, technical, policy, market dynamics, and environmental. We explore how these parameters were considered in the reviewed studies and propose ways and specific examples of addressing the dynamic effects in the criticality indicators. Furthermore, we discuss the current work on future scenarios to provide reference points for indicator benchmarks. The insights and guidelines derived from the review and our recommendations for future research set the foundations for an enhanced dynamic and site-specific criticality assessment framework.