Well-defined atomically dispersed metal catalysts (or single-atom catalysts) have been widely studied to fundamentally understand their catalytic mechanisms, improve the catalytic efficiency, increase the abundance of active components, enhance the catalyst utilization, and develop cost-effective catalysts to effectively reduce the usage of noble metals. Such single-atom catalysts have relatively higher selectivity and catalytic activity with maximum atom utilization due to their unique characteristics of high metal dispersion and a low-coordination environment. However, freestanding single atoms are thermodynamically unstable, such that during synthesis and catalytic reactions, they inevitably tend to agglomerate to reduce the system energy associated with their large surface areas. Therefore, developing innovative strategies to stabilize single-atom catalysts, including mass-separated soft landing, one-pot pyrolysis, co-precipitation, impregnation, atomic layer deposition, and organometallic complexation, is critically needed. Many types of supporting materials, including polymers, have been commonly used to stabilize single atoms in these fabrication techniques. Herein, we review the stabilization strategies of single-atom catalyst, including different synthesis methods, specific metals and carriers, specific catalytic reactions, and their advantages and disadvantages. In particular, this review focuses on the application of polymers in the synthesis and stabilization of single-atom catalysts, including their functions as carriers for metal single atoms, synthetic templates, encapsulation agents, and protection agents during the fabrication process. The technical challenges that are currently faced by single-atom catalysts are summarized, and perspectives related to future research directions including catalytic mechanisms, enhancement of the catalyst loading content, and large-scale implementation are proposed to realize their practical applications. Graphical Abstract Single-atom catalysts are characterized by high metal dispersibility, weak coordination environments, high catalytic activity and selectivity, and the highest atom utilization. However, due to the free energy of the large surface area, individual atoms are usually unstable and are prone to agglomeration during synthesis and catalytic reactions. Therefore, researchers have developed innovative strategies, such as soft sedimentation, one-pot pyrolysis, coprecipitation, impregnation, step reduction, atomic layer precipitation, and organometallic complexation, to stabilize single-atom catalysts in practical applications. This article summarizes the stabilization strategies for single-atom catalysts from the aspects of their synthesis methods, metal and support types, catalytic reaction types, and its advantages and disadvantages. The focus is on the application of polymers in the preparation and stabilization of single-atom catalysts, including metal single-atom carriers, synthetic templates, encapsulation agents, and the role of polymers as protection agents in the manufacturing process. The main feature of polymers and polymer-derived materials is that they usually contain abundant heteroatoms, such as N, that possess lone-pair electrons. These lone-pair electrons can anchor the single metal atom through strong coordination interactions. The coordination environment of the lone-pair electrons can facilitate the formation of single-atom catalysts because they can enlarge the average distance of a single precursor adsorbed on the polymer matrix. Polymers with nitrogen groups are favorable candidates for dispersing active single atoms by weakening the tendency of metal aggregation and redistributing the charge densities around single atoms to enhance the catalytic performance. This review provides a summary and analysis of the current technical challenges faced by single-atom catalysts and future research directions, such as the catalytic mechanism of single-atom catalysts, sufficiently high loading, and large-scale implementation.