Rare-earth elements (REEs) — comprising the 15 lanthanides together with scandium and yttrium — are indispensable to the technologies driving the global energy and digital transition. Neodymium-iron-boron permanent magnets power electric vehicle motors and wind turbine generators; europium and terbium phosphors underpin LED and fluorescent lighting; lanthanum enables nickel-metal hydride batteries; gadolinium serves as a contrast agent in magnetic resonance imaging; and cerium and lanthanum are essential catalysts in petroleum refining and automotive catalytic converters. Despite their collective name, rare-earth elements are not geochemically rare — cerium is as abundant as copper in Earth's crust — but their dispersed occurrence, chemically similar behaviour, and the environmental and radiological complexity of their extraction and separation make them among the most strategically sensitive materials in the global economy. This chapter reviews the descriptive chemistry of all 17 REEs, their physical and chemical properties, their principal applications across ten industrial domains, and — critically — the sustainability dimensions of their supply chain: the environmental consequences of mining, the geopolitical concentration of processing capacity in China, and the state of recycling technology and circular economy strategies for recovering REEs from end-of-life products. The chapter closes with an analysis of the policy and industrial responses to REE supply chain vulnerability in the European Union, the United States, and Japan.