The SAT problem solving algorithms are an important research area in computer science aimed at solving the Boolean satisfiability problem. With the wide application of SAT problems in the fields of hardware design, automated planning, and artificial intelligence, researchers have proposed a variety of efficient solution algorithms. The classical algorithms include exhaustive search and backtracking search, but they are less efficient when dealing with large-scale problems. Heuristic search methods accelerate the search process by introducing randomization or evolutionary algorithms to improve the solution efficiency. Learning-based methods utilize learning and memorizing the explored search space or learning heuristic information to guide the search process. The CDCL algorithm, on the other hand, is an efficient conflict-driven learning algorithm that achieves impressive results by learning and applying conflict information to prune the search space. Parallel and distributed solving as well as quantum computing methods are hot research topics in recent years, which provide new ideas and technical support for solving large-scale problems. The research on algorithms for solving SAT problems continues to innovate, providing powerful tools and technical support for real-world problem solving.