Spermatogonial stem cells (SSCs) are crucial for maintaining spermatogenesis throughout life, and understanding how these cells function has important implications for understanding male infertility. Recently, various populations of cells harbouring stem cell-like properties have been identified in rodent seminiferous tubules, but deciphering how these cells might fuel spermatogenesis has been difficult, and various models to explain SSC dynamics have been put forward. This Review provides an overview of the organization and timing of spermatogenesis and then discusses these models in light of recent studies of SSC markers, heterogeneity and cell division dynamics, highlighting the evidence for and against each model.