The coordination of cell proliferation and differentiation is central to the development and maintenance of tissues, while its dysregulation underlies the transition to diseased states. By combining lineage tracing with transcriptional profiling and marker-based assays, statistical methods are delivering insights into the dynamics of stem cells and their developmental precursors. These studies have provided evidence for molecular heterogeneity and fate priming, and have revealed a role for stochasticity in stem cell fate, refocusing the search for regulatory mechanisms. At the same time, they present a quantitative platform to study the initiation and progression of disease. Here, we review how quantitative lineage tracing strategies are shaping our understanding of the cellular mechanisms of tissue development, maintenance and disease.