求解公式的可满足性在诸如形式化验证、电子设计自动化与人工智能等众多领域中都具有非常重要的理论与应用价值，成为近年来的研究热点。本文针对命题公式与一阶公式的可满足性问题，重点介绍了布尔可满足性与可满足性模理论求解技术的基本原理，并且根据算法的类型进行分类阐述，分析了各种算法的优缺点。最后，讨论了目前面临的主要挑战，对今后的研究方向进行了展望。

Solving the satisfiability of formulae is theoretically important in the practical applications of various fields, such as formal verification, electronic design automation and artificial intelligence. This paper introduces the principles of the Boolean Satisfiability and Satisfiability Modulo Theories. The existing algorithms are introduced and compared according to their types. The qualities of these algorithms are also analyzed. Finally, we discuss the current challenges, and outline the future research trend.