Patients with inflammatory bowel disease have an increased risk of developing colorectal cancer, and this risk is related to disease duration, extent, and cumulative inflammation burden. Carcinogenesis follows the principles of Darwinian evolution, whereby somatic cells acquire genomic alterations that provide them with a survival and/or growth advantage. Colitis represents a unique situation whereby routine surveillance endoscopy provides a serendipitous opportunity to observe somatic evolution over space and time in a human organ. Moreover, somatic evolution in colitis is evolution in the 'fast lane': the repeated rounds of inflammation and mucosal healing that are characteristic of the disease accelerate the evolutionary process and likely provide a strong selective pressure for inflammation-adapted phenotypic traits. In this review, we discuss the evolutionary dynamics of pre-neoplastic clones in colitis with a focus on how measuring their evolutionary trajectories could deliver a powerful way to predict future cancer occurrence. Measurements of somatic evolution require an interdisciplinary approach that combines quantitative measurement of the genotype, phenotype and the microenvironment of somatic cells-paying particular attention to spatial heterogeneity across the colon-together with mathematical modeling to interpret these data within an evolutionary framework. Here we take a practical approach in discussing how and why the different "evolutionary ingredients" can and should be measured, together with our viewpoint on subsequent translation into clinical practice. We highlight the open questions in the evolution of colitis-associated cancer as a stimulus for future work.