Cancer research encompasses data across various scales, modalities, and resolutions, from screening and diagnostic imaging to digitized histopathology slides to various types of molecular data and clinical records. The integration of these diverse data types for personalized cancer care and predictive modeling holds the promise of enhancing the accuracy and reliability of cancer screening, diagnosis, and treatment. Traditional analytical methods, which often focus on isolated or unimodal information, fall short of capturing the complex and heterogeneous nature of cancer data. The advent of deep neural networks has spurred the development of sophisticated multimodal data fusion techniques capable of extracting and synthesizing information from disparate sources. Among these, Graph Neural Networks (GNNs) and Transformers have emerged as powerful tools for multimodal learning, demonstrating significant success. This review presents the foundational principles of multimodal learning including oncology data modalities, taxonomy of multimodal learning, and fusion strategies. We delve into the recent advancements in GNNs and Transformers for the fusion of multimodal data in oncology, spotlighting key studies and their pivotal findings. We discuss the unique challenges of multimodal learning, such as data heterogeneity and integration complexities, alongside the opportunities it presents for a more nuanced and comprehensive understanding of cancer. Finally, we present some of the latest comprehensive multimodal pan-cancer data sources. By surveying the landscape of multimodal data integration in oncology, our goal is to underline the transformative potential of multimodal GNNs and Transformers. Through technological advancements and the methodological innovations presented in this review, we aim to chart a course for future research in this promising field. This review may be the first that highlights the current state of multimodal modeling applications in cancer using GNNs and transformers, presents comprehensive multimodal oncology data sources, and sets the stage for multimodal evolution, encouraging further exploration and development in personalized cancer care.