Recent clinical success with metal-based radiopharmaceuticals has sparked an interest in the potential of these drugs for personalized medicine. Although often overlooked, the success and global impact of nuclear medicine is contingent upon the purity and availability of medical isotopes, commonly referred to as radiometals. For nuclear medicine to reach its true potential and change patient lives, novel production and purification techniques that increase inventory of radiometals are desperately needed. This tutorial review serves as a resource for those both new and experienced in nuclear medicine by providing a detailed explanation of the foundations for the production and purification of radiometals, stemming from nuclear physics, analytical chemistry, and so many other fields, all in one document. The fundamental science behind targetry, particle accelerators, nuclear reactors, nuclear reactions, and radiochemical separation are presented in the context of the field. Finally, a summary of the latest breakthroughs and a critical discussion of the threats and future potential of the most utilized radiometals is also included. With greater understanding of the fundamentals, fellow scientists will be able to better interpret the literature, identify knowledge gaps or problems and ultimately invent new production and purification pathways to increase the global availability of medical isotopes.