A guide to understanding tumour evolution through the lens of population genetics.

Every cancer carries the history of its own evolution, hidden in its genome. Modern DNA sequencing can catalogue millions of mutations and profile tumours across space and time, but sequencing alone struggles to answer the questions that matter most: when did key adaptations emerge, how strongly were they selected, why do some tumours relapse whereas others do not, and how will the cancer evolve next? The reason is fundamental: sequencing is a snapshot, whereas evolution is a dynamic process. Bridging this gap requires moving beyond descriptive cancer genomics towards quantitative evolutionary inference. In this Review, we argue that population genetics provides the mathematical framework needed to extract evolutionary dynamics from cancer genomes. We show how models of mutation, selection and drift transform allele frequencies from descriptive measurements into quantitative estimates of clonal fitness and evolutionary timings. We discuss how these principles extend to epigenetic inheritance, plasticity and ecological interactions within the tumour ecosystem, and examine the assumptions and limitations for their application to modern sequencing data. By reframing cancer genomes as quantitative records of evolutionary processes rather than catalogues of mutations, researchers have used population genetics to provide a foundation for understanding - and ultimately predicting - the trajectories of cancer evolution.