With the development of hyperspectral sensors, more and more hyperspectral images can be acquired, and the pixel-oriented classification of hyperspectral images has attracted the attention of many researchers. However, accurately classifying pixels is challenging due to the limited labeling data and the high feature dimension of hyperspectral images. Graph Convolutional Network (GCN) based methods offer a new research direction for hyperspectral image classification due to their exceptional ability to handle irregular data. GCN uses nodes to represent samples and edges to represent relationships between nodes. Graph convolution operations enable information propagation between nodes, capturing complex associations and facilitating node classification. The GCN-based approach has demonstrated significant potential in hyperspectral image classification due to its ability to effectively extract spectral features from such images. This paper presents a comprehensive review of GCN-based hyperspectral image classification methods. The review covers five aspects: research background, traditional hyperspectral classification methods, mainstream GCN-based hyperspectral classification methods, challenges and limitations, and future developments. With the continuous development of GCN methods, hyperspectral image classification is expected to achieve higher accuracy and wider application in various fields.