Fifteen years ago, it was proposed that the cell cycle in fission yeast can be driven by quantitative changes in the activity of a single protein kinase complex comprising a cyclin - namely cyclin B - and cyclin dependent kinase 1 (Cdk1). When its activity is low, Cdk1 triggers the onset of S phase; when its activity level exceeds a specific threshold, it promotes entry into mitosis. This model has redefined our understanding of the essential functional inputs that organize cell cycle progression, and its main principles now appear to be applicable to all eukaryotic cells. But how does a change in the activity of one kinase generate ordered progression through the cell cycle in order to separate DNA replication from mitosis? To answer this question, we must consider the biochemical processes that underlie the phosphorylation of Cdk1 substrates. In this Commentary, we discuss recent findings that have shed light on how the threshold levels of Cdk1 activity that are required for progression through each phase are determined, how an increase in Cdk activity generates directionality in the cell cycle, and why cell cycle transitions are abrupt rather than gradual. These considerations lead to a general quantitative model of cell cycle control, in which opposing kinase and phosphatase activities have an essential role in ensuring dynamic transitions.