Abstract <p>When the Materials Research Society teamed with the American Physical Society in 2010 to respond to the rare-earth crisis, there was no expectation of influencing federal legislation. However, the impact of the resulting report, Energy Critical Elements, reached even Congress and the President’s desk within three years, revealing surprising influence by the materials and physics communities. Following an overview of the methodology for materials criticality assessment, this review provides a history, punctuated by a series of crises, of critical materials in national security. More quantitative ways to measure risk and importance are needed in assessments; a promising statistical approach based on a geologic entropy function is developed with examples illustrating how flexible constraints–such as economic, national security related, or regulatory–can be applied. The formulation describes the relation between elemental price and crustal abundance for selected elements, both important to supply risk.</p> Graphical abstract <p>Data of price (US$/kg) vs mined mass (metric tons) for 39 chemical elements showing a power-law relationship. The theory fitting the data is based on a geologic entropy with a price constraint.</p>