The coordination of growth, DNA replication and division in proliferating cells can be adequately explained by a 'clock + checkpoint' model. The clock is an underlying cyclical sequence of states; the checkpoints ensure that the cycle proceeds without mistakes. From the molecular complexities of the control system in modern eukaryotes, we isolate a simple network of positive and negative feedbacks that embodies a 'clock + checkpoints'. The model accounts for the fundamental physiological properties of mitotic cell divisions, evokes a new view of the meiotic program, and suggests how the control system may have evolved in the first place.