Single-atom catalysts are emerging as a frontier due to their unique structural properties, which result from the isolation of active sites. The dispersion of isolated atoms ensures even distribution of reactants, promoting good contact between the catalyst and reactants, and leading to significant improvements in catalytic activity and efficiency. The active site can be rationally modified by altering the metal center to influence catalytic behavior and performance. To understand the dynamic changes of single atoms, the concepts related to their geometrical configuration and electronic structure are introduced. Therefore, a comprehensive overview of the development of single-atom catalysts emphasizes the role of the isolated active site in a single-atom catalyst. Understanding the structure-activity relationship is crucial for developing single-atom active sites with optimal dispersion, thereby enabling advanced methods for designing catalysts tailored to specific catalytic processes. Challenges and outlooks for single-atom catalysts are briefly discussed.