For tumours to develop, mutations must disrupt tissue homeostasis in favour of deregulated proliferation. Genetic lineage tracing has uncovered the behaviour of proliferating cells that underpins the maintenance of epithelial tissues and the barriers that are broken in neoplastic transformation. In this Review, we focus on new insights revealed by quantifying the behaviour of normal, preneoplastic and tumour cells in epithelia in transgenic mice and consider their potential importance in humans.