The cell division cycle can be modelled as a series of quantitative thresholds of cyclin-dependent kinase (CDK) activity. DNA synthesis has a lower threshold requirement for CDK than does entry into mitosis, and mitotic exit and re-setting of replication origins occur upon collapse of CDK activity below both thresholds, so that the simple rise and fall of CDK with each cell cycle might suffice to ensure repeated alternation of chromosome duplication and segregation. Recent experimental dissections of mitotic exit, which have both guided and been informed by computational modelling, suggest a more complicated mechanism, in which unidirectional progression is ensured by systems-level control of CDK function and the balance between mitotic CDK and phosphatase activities.