Noble metals have received widespread applications in the field of catalysis due to their unique intrinsic properties and irreplaceable catalytic activities. However, in consideration of the scarcity and high cost, maximizing the efficiency of noble metals for catalysis is of prime importance in the societal pursuit of sustainable energy. In recent years, noble-metal single-atom catalysts (NMSACs) with well-defined structures have gained great research attention due to their maximum atom utilization efficiency (100%), distinct active sites and high catalytic activity and selectivity. This review comprehensively discusses the recent advancements in NMSACs for catalytic applications. Firstly, various fabrication strategies for NMSACs are introduced with a focus on how to effectively stabilize single noble-metal atoms on appropriate substrates and prevent their migration and aggregation. Subsequently, some advanced characterization techniques are presented to precisely probe the noble-metal active sites at the atomic level, which is critical to investigate the structure of NMSACs. Furthermore, we provide a comprehensive summary of various types of NMSACs for the applications of thermocatalysis, electrocatalysis, and photocatalysis, with special emphasis on the structure–activity relationships and the underlying catalytic mechanisms. Finally, the remaining challenges and future opportunities are provided for guiding the rational design of advanced NMSACs toward various catalytic processes in the chemical transformation and energy conversion fields.