During embryonic and postnatal development, the different cells types that form adult tissues must be generated and specified in a precise temporal manner. During adult life, most tissues undergo constant renewal to maintain homeostasis. Lineage-tracing and genetic labelling technologies are beginning to shed light on the mechanisms and dynamics of stem and progenitor cell fate determination during development, tissue maintenance and repair, as well as their dysregulation in tumour formation. Statistical approaches, based on proliferation assays and clonal fate analyses, provide quantitative insights into cell kinetics and fate behaviour. These are powerful techniques to address new questions and paradigms in transgenic mouse models and other model systems.