Stem cells are fundamental to human life and offer great therapeutic potential, yet their biology remains incompletely-or in cases even poorly-understood. The field of stem cell biology has grown substantially in recent years due to a combination of experimental and theoretical contributions: the experimental branch of this work provides data in an ever-increasing number of dimensions, while the theoretical branch seeks to determine suitable models of the fundamental stem cell processes that these data describe. The application of population dynamics to biology is amongst the oldest applications of mathematics to biology, and the population dynamics perspective continues to offer much today. Here we describe the impact that such a perspective has made in the field of stem cell biology. Using hematopoietic stem cells as our model system, we discuss the approaches that have been used to study their key properties, such as capacity for self-renewal, differentiation, and cell fate lineage choice. We will also discuss the relevance of population dynamics in models of stem cells and cancer, where competition naturally emerges as an influential factor on the temporal evolution of cell populations.