With the rise of graph structured data mining, hypergraph, as a special type of graph structured data, is widely concerned in social network analysis, image processing, biological response analysis, and other fields. By analyzing the topological structure and node attributes of hypergraph, many problemscan be effectively solved such as recommendation, community detection, and so on. According to the characteristics of hypergraph learning algorithm, it can be divided into spectral analysis method, neural network method, and other method. According to the methods used to process hypergraphs, it can be further divided into expansion method and non-expansion method. If the expansion method is applied to the indecomposable hypergraph, it is likely to cause information loss. However, the existing hypergraph reviews do not discuss that hypergraph learning methods are applicable to which type of hypergraphs. So, this article discusses the expansion method and non-expansion method respectively from the aspects of spectral analysis method and neural network method, and further subdivides them according to their algorithm characteristics and application scenarios. Then, the ideas of different algorithms are analyzed and comparedin experiments. The advantages and disadvantages of different algorithms are concluded. Finally, some promising research directionsare proposed.