The mechanisms that regulate the balance between stem cell duplication and differentiation in adult tissues remain in debate. Using a combination of genetic lineage tracing and marker-based assays, the quantitative statistical analysis of clone size and cell composition has provided insights into the patterns of stem cell fate across a variety of tissue types and organisms. These studies have emphasized the role of niche factors and environmental cues in promoting stem cell competence, fate priming and stochastic renewal programs. At the same time, evidence for injury-induced “cellular reprogramming” has revealed the remarkable flexibility of cell states, allowing progenitors to reacquire self- renewal potential during regeneration. Together, these findings have questioned the nature of stem cell identity and function. Here, focusing on a range of canonical tissue types, we review how quantitative modelling-based approaches have uncovered conserved patterns of stem cell fate and provided new insights into the mechanisms that regulate self-renewal.