The fundamental processes of DNA synthesis, mitosis and cell division in eukaryotic cells are controlled by a complex network of interacting genes and proteins focused on periodic activation of a family of master regulators, the cyclin-dependent protein kinases (CDKs). This regulatory network must ensure the strict alternation of DNA synthesis (S phase) and mitosis (M phase) and the proper coordination of cell division with cell growth. Moreover, the control system must operate robustly in the face of considerable molecular noise that is unavoidable in the small confines of a yeast cell. After reviewing the basic molecular biology of the CDK regulatory network in budding yeast, I will examine the physiological consequences of the reaction mechanism by mathematical and computational modeling. Deterministic models (differential equations) describe the average behavior of populations of yeast cells, and stochastic models address issues of variability and robustness in individual cells. Both types of models will be evaluated in light of quantitative experimental observations.