The Boolean Satisfiability problem (SAT) is a classical problem in computer science and artificial intelligence, and the most widely studied NP-complete problem. It aims to determine whether there exists an assignment of a value to a variable of a given Boolean formula that makes the formula true. In recent years, with the continuous improvement of theoretical research and practical application needs, the research on SAT problems has achieved remarkable results. These advances have not only promoted the in-depth study of the SAT problem itself, but also provided strong support for the development of computer science, artificial intelligence and other related fields. Currently, the research of SAT problem involves several aspects, this paper mainly focuses on the three aspects of the improvement of SAT solving algorithm, the deepening of the theoretical foundation of SAT and the expansion of the application area to sort out the related research results, summarize the limitations of the existing methods, and propose possible future work.