The evolutionary events that cause colorectal adenomas (benign) to progress to carcinomas (malignant) remain largely undetermined. Using multi-region genome and exome sequencing of 24 benign and malignant colorectal tumours, we investigate the evolutionary fitness landscape occupied by these neoplasms. Unlike carcinomas, advanced adenomas frequently harbour sub-clonal driver mutations-considered to be functionally important in the carcinogenic process-that have not swept to fixation, and have relatively high genetic heterogeneity. Carcinomas are distinguished from adenomas by widespread aneusomies that are usually clonal and often accrue in a 'punctuated' fashion. We conclude that adenomas evolve across an undulating fitness landscape, whereas carcinomas occupy a sharper fitness peak, probably owing to stabilizing selection.