Endohedral metallofullerenes (EMFs), a new class of hybrid molecules formed by encapsulation of metallic species inside fullerene cages, exhibit unique properties that differ distinctly from those of empty fullerenes because of the presence of metals and their hybridization effects via electron transfer. This critical review provides a balanced but not an exhaustive summary regarding almost all aspects of EMFs, including the history, the classification, current progress in the synthesis, extraction, isolation, and characterization of EMFs, as well as their physiochemical properties and applications in fields such as electronics, photovoltaics, biomedicine, and materials science. Emphasis is assigned to experimentally obtained results, especially the X-ray crystallographic characterizations of EMFs and their derivatives, rather than theoretical calculations, although the latter has indeed enhanced our knowledge of metal-cage interactions. Finally, perspectives related to future developments and challenges in the research of EMFs are proposed. (381 references).