Graph neural networks (GNNs), as topology/structure-aware models within deep learning, have emerged as powerful tools for AI-aided drug discovery (AIDD). By directly operating on molecular graphs, GNNs offer an intuitive and expressive framework for learning the complex topological and geometric features of drug-like molecules, cementing their role in modern molecular modeling. This review provides a comprehensive overview of the methodological foundations and representative applications of GNNs in drug discovery, spanning tasks such as molecular property prediction, virtual screening, molecular generation, biomedical knowledge graph construction, and synthesis planning. Particular attention is given to recent methodological advances, including geometric GNNs, interpretable models, uncertainty quantification, scalable graph architectures, and graph generative frameworks. We also discuss how these models integrate with modern deep learning approaches, such as self-supervised learning, multi-task learning, meta-learning and pre-training. Throughout this review, we highlight the practical challenges and methodological bottlenecks encountered when applying GNNs to real-world drug discovery pipelines, and conclude with a discussion on future directions.