Drug side effect prediction plays a crucial role in molecular structure optimization, dose adjustment, and the development of personalized medication strategies, representing an essential component of modern drug research pipelines and clinical medication management. Intelligent computational methods can effectively overcome the limitations inherent in traditional prediction approaches, such as high costs and prolonged development cycles. As an emerging deep learning paradigm capable of effectively modeling graph-structured data, graph neural networks (GNNs) can capture complex relationships between drug molecular structures and biological systems, thereby enhancing the accuracy and generalizability of side-effect prediction models. This article provides a comprehensive review of recent advances in GNN-based drug side effect prediction and discusses potential future research directions in this field.