AbstractWith the development of deep learning on high-order correlations, hypergraph neural networks have received much attention in recent years. Generally, the neural networks on hypergraph can be divided into two categories, including the spectral-based methods and the spatial-based methods. For the spectral-based methods, the convolution operation is formulated in the spectral domain of graph, and we introduce the typical spectral-based methods, including hypergraph neural networks (HGNN), hypergraph convolution with attention (Hyper-Atten), and hyperbolic hypergraph neural network (HHGNN), which extend hypergraph computation to hyperbolic spaces beyond the Euclidean space. For the spatial-based methods, the convolution operation is defined in groups of spatially close vertices. We then present spatial-based hypergraph neural networks of the general hypergraph neural networks (HGNN+) and the dynamic hypergraph neural networks (DHGNN). Additionally, there are several convolution methods that attempt to reduce the hypergraph structure to the graph structure, so that the existing graph convolution methods can be directly deployed. Lastly, we analyze the association and comparison between hypergraph and graph in the two areas described above (spectral-based, spatial-based), further demonstrating the ability and advantages of hypergraph on constructing and computing higher-order correlations in the data.