The eukaryotic cell division cycle encompasses an ordered series of events. Chromosomal DNA is replicated during S phase of the cell cycle before being distributed to daughter cells in mitosis. Both S phase and mitosis in turn consist of an intricately ordered sequence of molecular events. How cell cycle ordering is achieved, to promote healthy cell proliferation and avert insults on genomic integrity, has been a theme of Paul Nurse's research. To explain a key aspect of cell cycle ordering, sequential S phase and mitosis, Stern & Nurse proposed 'A quantitative model for cdc2 control of S phase and mitosis in fission yeast'. In this model, S phase and mitosis are ordered by their dependence on increasing levels of cyclin-dependent kinase (Cdk) activity. Alternative mechanisms for ordering have been proposed that rely on checkpoint controls or on sequential waves of cyclins with distinct substrate specificities. Here, we review these ideas in the light of experimental evidence that has meanwhile accumulated. Quantitative Cdk control emerges as the basis for cell cycle ordering, fine-tuned by cyclin specificity and checkpoints. We propose a molecular explanation for quantitative Cdk control, based on thresholds imposed by Cdk-counteracting phosphatases, and discuss its implications.