Making decisions on how best to treat cancer patients requires the integration of different data sets, including genomic profiles, tumour histopathology, radiological images, proteomic analysis and more. This wealth of biological information calls for novel strategies to integrate such information in a meaningful, predictive and experimentally verifiable way. In this Perspective we explain how executable computational models meet this need. Such models provide a means for comprehensive data integration, can be experimentally validated, are readily interpreted both biologically and clinically, and have the potential to predict effective therapies for different cancer types and subtypes. We explain what executable models are and how they can be used to represent the dynamic biological behaviours inherent in cancer, and demonstrate how such models, when coupled with automated reasoning, facilitate our understanding of the mechanisms by which oncogenic signalling pathways regulate tumours. We explore how executable models have impacted the field of cancer research and argue that extending them to represent a tumour in a specific patient (that is, an avatar) will pave the way for improved personalized treatments and precision medicine. Finally, we highlight some of the ongoing challenges in developing executable models and stress that effective cross-disciplinary efforts are key to forward progress in the field.