Metal-organic frameworks (MOFs) are a class of distinctive porous crystalline materials constructed by metal ions/clusters and organic linkers. Owing to their structural diversity, functional adjustability, and high surface area, different types of MOF-based single metal sites are well exploited, including coordinately unsaturated metal sites from metal nodes and metallolinkers, as well as active metal species immobilized to MOFs. Furthermore, controllable thermal transformation of MOFs can upgrade them to nanomaterials functionalized with active single-atom catalysts (SACs). These unique features of MOFs and their derivatives enable them to serve as a highly versatile platform for catalysis, which has actually been becoming a rapidly developing interdisciplinary research area. In this review, we overview the recent developments of catalysis at single metal sites in MOF-based materials with emphasis on their structures and applications for thermocatalysis, electrocatalysis, and photocatalysis. We also compare the results and summarize the major insights gained from the works in this review, providing the challenges and prospects in this emerging field.