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The application of data science in cancer research has been boosted by major advances in three primary areas: (1) Data: diversity, amount, and availability of biomedical data; (2) Advances in Artificial Intelligence (AI) and Machine Learning (ML) algorithms that enable learning from complex, large-scale data; and (3) Advances in computer architectures allowing unprecedented acceleration of simulation and machine learning algorithms. These advances help build in silico ML models that can provide transformative insights from data including: molecular dynamics simulations, next-generation sequencing, omics, imaging, and unstructured clinical text documents. Unique challenges persist, however, in building ML models related to cancer, including: (1) access, sharing, labeling, and integration of multimodal and multi-institutional data across different cancer types; (2) developing AI models for cancer research capable of scaling on next generation high performance computers; and (3) assessing robustness and reliability in the AI models. In this paper, we review the National Cancer Institute (NCI) -Department of Energy (DOE) collaboration, Joint Design of Advanced Computing Solutions for Cancer (JDACS4C), a multi-institution collaborative effort focused on advancing computing and data technologies to accelerate cancer research on three levels: molecular, cellular, and population. This collaboration integrates various types of generated data, pre-exascale compute resources, and advances in ML models to increase understanding of basic cancer biology, identify promising new treatment options, predict outcomes, and eventually prescribe specialized treatments for patients with cancer.