Next-generation cancer and oncology research needs to take full advantage of the multimodal structured, or graph, information, with the graph data types ranging from molecular structures to spatially resolved imaging and digital pathology, biological networks, and knowledge graphs. Graph Neural Networks (GNNs) efficiently combine the graph structure representations with the high predictive performance of deep learning, especially on large multimodal datasets. In this review article, we survey the landscape of recent (2020–present) GNN applications in the context of cancer and oncology research, and delineate six currently predominant research areas. We then identify the most promising directions for future research. We compare GNNs with graphical models and “non-structured” deep learning, and devise guidelines for cancer and oncology researchers or physician-scientists, asking the question of whether they should adopt the GNN methodology in their research pipelines.