This paper brings a discussion on the current state-of-the-art in criticality assessment in an international context. It analyzes the status of resource criticality concepts and their calculation methods. The current practice often exhibits a common two-axis assessment framework but the way the two axes are further operationalized shows heterogeneous approaches. Apart from the two-axis as key element of criticality assessment, the scope of the materials, the role of substitution, the delineation of the supply chain and data, and indicator selection are addressed as key elements. The abovementioned criticality assessment practice is approached in function of the upcoming international debate on criticality. The paper tackles the role of criticality assessment in the context of the sustainability assessment toolbox and it proposes a clear distinction between criticality assessment and resilience to criticality. The insights offered in the paper may feed the international discussion in the identification of elements that may be harmonized and elements that may be better left open in function of the particular application. Display omitted •Current criticality assessment practice in the international context is analyzed.•The practice is approached in function of the upcoming international debate.•The paper identifies elements that may be harmonized.•Equally, it discusses elements that may be better left open.