Stem cells and their descendents are the building blocks of life. How stem cell populations guarantee their maintenance and/or self-renewal, and how individual stem cells decide to transit from one cell stage to another to generate different cell types are long-standing and fascinating questions in the field. Here, we review the discussions that took place at a recent EMBO conference in Cambridge, UK, in which these questions were placed in the context of the latest advances in stem cell biology in presentations that covered stem cell heterogeneity, cell fate decision-making, induced pluripotency, as well as the mathematical modelling of these phenomena.