In the tail of growing vertebrate embryos exists a territory called the progenitor zone, containing stem cells that give rise to mesodermal (future muscles and bones) and neural cells (future nervous system). While the embryo is extending in a head-to-tail manner, these cells self-renew and continuously provide the cellular material that will become the blueprint of our body. We recently highlighted, within this cell population, cell-to-cell variations in expression levels of key transcription factors involved in progenitor fate specification. We also found that differences in expression levels of these factors regulate the choice of stem cells to stay in their niche or to migrate into neural and mesodermal tissues. Mathematical modeling then revealed cell-to-cell heterogeneity in the progenitor territory as a key parameter in regulating cells rearrangement and tissue morphogenesis. Our project is now to better understand how specification and morphogenetic programs are intertwined during axis extension.