With the increasing scale and complexity of computer networks, it is difficult for network administrators to ensure that the network intent has been correctly realized, and the incorrect network configuration will affect the security and availability of the network. Inspired by the successful application of formal methods in the field of hardware verification and software verification, researchers applied formal methods to networks, forming a new research field, namely network verification, which aims to use rigorous mathematical methods to prove the correctness of the network. Network verification has become a hot research topic in the field of network and security, and its research results have been successfully applied in actual networks. From the three research directions of data plane verification, control plane verification, and stateful network verification, this study systematically summarizes the existing research results in the field of network verification, and analyzes the research hotspots and related solutions, aiming to organize the field of network verification and provides systematic references and future work prospects for researchers in the field.