In recent years, sophisticated fate-mapping tools have been developed to study the behavior of stem cells in the intact organism. These experimental approaches are beginning to yield a quantitative picture of how cell numbers are regulated during steady state and in response to challenges. Focusing on hematopoiesis and immune responses, we discuss how novel mathematical approaches driven by these fate-mapping data have provided insights into the dynamics and topology of cellular differentiation pathways in vivo. The combination of experiment and theory has allowed to quantify the degree of self-renewal in stem and progenitor cells, shown how native hematopoiesis differs fundamentally from post-transplantation hematopoiesis, and uncovered that the diversification of T lymphocytes during immune responses resembles tissue renewal driven by stem cells.
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