Hyperspectral images provide rich spectral-spatial information but pose significant classification challenges due to high dimensionality, noise, mixed pixels, and limited labeled samples. Graph Neural Networks (GNNs) have emerged as a promising solution, offering a semi-supervised framework that can capture complex spatial-spectral relationships inherent in non-Euclidean hyperspectral image data. However, existing reviews often concentrate on specific aspects, thus limiting a comprehensive understanding of GNN-based hyperspectral image classification. This review systematically outlines the fundamental concepts of hyperspectral image classification and GNNs, and summarizes leading approaches from both traditional machine learning and deep learning. Then, it categorizes GNN-based methods into four paradigms: graph recurrent neural networks, graph convolutional networks, graph autoencoders, and hybrid graph neural networks, discussing their theoretical underpinnings, architectures, and representative applications. Finally, five key directions are further highlighted: adaptive graph construction, dynamic graph processing, deeper architectures, self-supervised strategies, and robustness enhancement. These insights aim to facilitate continued innovation in GNN-based hyperspectral imaging, guiding researchers toward more efficient and accurate classification frameworks.