The term “critical raw materials” (CRMs) refers to various metals and nonmetals that are crucial to Europe’s economic progress. Modern technologies enabling effective use and recyclability of CRMs are in critical demand for the EU industries. The use of CRMs, especially in the fields of biomedicine, aerospace, electric vehicles, and energy applications, is almost irreplaceable. Additive manufacturing (also referred to as 3D printing) is one of the key enabling technologies in the field of manufacturing which underpins the Fourth Industrial Revolution. 3D printing not only suppresses waste but also provides an efficient buy-to-fly ratio and possesses the potential to entirely change supply and distribution chains, significantly reducing costs and revolutionizing all logistics. This review provides comprehensive new insights into CRM-containing materials processed by modern additive manufacturing techniques and outlines the potential for increasing the efficiency of CRMs utilization and reducing the dependence on CRMs through wider industrial incorporation of AM and specifics of powder bed AM methods making them prime candidates for such developments.