Explore mathematical modeling approaches to cancer research in this comprehensive lecture by Helen Byrne from the International Centre for Theoretical Sciences. Delve into the evolution of cancer understanding, from ancient Egyptian papyri to recent breakthrough clinical trials. Discover how advanced sequencing, imaging techniques, and computational methods are revolutionizing cancer research. Learn about the application of theoretical tools in understanding and controlling cancer progression, designing clinical trials, and their potential for translational impact. Examine topics such as age-structured population theory, cancer network systems biology, heterogeneous population dynamics modeling, and machine learning techniques in cancer research. Gain insights into interpreting and utilizing diverse data sources to advance cancer treatment strategies and outcomes.