Recently, one type of mesoscale structure called core-periphery (CP) structure has received much attention in complex networks, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. The core-periphery structure refers to that core nodes are densely interconnected, while periphery nodes are connected to core nodes to different extents, and periphery nodes are sparsely interconnected. Core-periphery structure containing a single core or multiple cores has been identified in various networks. However, investigation of the detection problems of the core-periphery has not been summarized in the literature. In this paper, we first introduce the definition of the core-periphery structure. The core-periphery structure has been paid more and more attention by researchers in various fields since its introduction, and it has been proved to be a powerful tool to analyze the theory of various topologies in our society, we briefly expounded the application of core-periphery structure in economics, sociology, medicine and other fields, and revealed the huge development potential of this theory. Then, we give a detailed overview of classical detection algorithms since the core-periphery structure theory was proposed. Finally, we give the development characteristics and the possible research directions of the core-periphery detection algorithm.