Distributed systems play an important role in computing environments. Consensus protocols are employed to guarantee consistency among nodes. Design errors in the consensus protocols might cause failure in system operation and bring catastrophic consequences to humans and the environment. Therefore, it is important to prove the correctness of consensus protocols. Formal verification can strictly prove the correctness of target properties in designed models, which is suitable for verifying consensus protocols. However, the expanding scale of distributed systems results in more complicated issues and challenges to formal verification of consensus protocols. The method for formal verification of the consensus protocol design and increase in the verification scale are significant research issues in the formal verification of consensus protocols. This study investigates the current research on the employment of formal methods to verify consensus protocols, summarizes the key modeling methods and verification technologies, and proposes future research directions in this field.