As a complementary technology to Binary Decision Diagram-based(BDD-based) symbolic model checking, the verification techniques on Boolean satisfiability problem have gained an increasing wide of applications over the last few decades, which brings a dramatic improvement for automatic verification. In this paper, we firstly introduce the theory about the Boolean satisfiability verification, including the description on the problem of Boolean satisfiability verification, Davis-Putnam-Logemann-Loveland(DPLL) based complete verification algorithm, and all kinds of solvers generated and the logic languages used by those solvers. Moreover, we formulate a large number optimizations of technique revolutions based on Boolean SATisfiability(SAT) and Satisfiability Modulo Theories(SMT) solving in detail, including incomplete methods such as bounded model checking, and other methods for concurrent programs model checking. Finally, we point out the major challenge pervasively in industrial practice and prospect directions for future research in the field of formal verification. As a complementary technology to Binary Decision Diagram-based (BDD-based) symbolic model checking, the verification techniques on Boolean satisfiability problem have gained an increasing wide of applications over the last few decades, which brings a dramatic improvement for automatic verification. paper, we incorporated introduce the theory about the Boolean satisfiability verification, including the description on the problem of Boolean satisfiability verification, Davis-Putnam-Logemann-Loveland (DPLL) based complete verification algorithm, and all kinds of solvers generated and the logic languages ​​used by those solvers. Moreover, we formulate a large number optimizations of technique revolutions based on Boolean SAT satisfaction (SAT) and Satisfiability Modulo Theories (SMT) solving in detail, including incomplete methods such as bounded model checking, and other methods for concurrent programs model checking Finally, we point out the major challenge pervasively in industrial practice and prospect directions for future research in the field of formal verification.