Boolean satisfiability solvers, often referred to as SAT solvers, are algorithms designed to determine if a given Boolean formula can be satisfied by some assignment of true or false values to its variables. They play a crucial role in various fields, including computer science, artificial intelligence, and formal verification, by helping to solve problems that can be expressed in logical terms. These solvers work by exploring possible combinations of variable assignments and using techniques like backtracking, clause learning, and heuristics to efficiently find a solution or prove that none exists. Their effectiveness has made them essential tools in areas such as hardware design and software testing.