The burgeoning accumulation of large-scale biomedical data in oncology, alongside significant strides in deep learning (DL) technologies, has established multimodal DL (MDL) as a cornerstone of precision oncology. This review provides an overview of MDL applications in this field, based on an extensive literature survey. In total, 651 articles published before September 2024 are included. We first outline publicly available multimodal datasets that support cancer research. Then, we discuss key DL training methods, data representation techniques, and fusion strategies for integrating multimodal data. The review also examines MDL applications in tumor segmentation, detection, diagnosis, prognosis, treatment selection, and therapy response monitoring. Finally, we critically assess the limitations of current approaches and propose directions for future research. By synthesizing current progress and identifying challenges, this review aims to guide future efforts in leveraging MDL to advance precision oncology.