Repetitive cell cycles, which are essential to the perpetuation of life, are orchestrated by an underlying biochemical reaction network centered around cyclin-dependent protein kinases (Cdks) and their regulatory subunits (cyclins). Oscillations of Cdk1/CycB activity between low and high levels during the cycle trigger DNA replication and mitosis in the correct order. Based on computational modeling, we proposed that the low and the high kinase activity states are alternative stable steady states of a bistable Cdk-control system. Bistability is a consequence of system-level feedback (positive and double-negative feedback signals) in the underlying control system. We have also argued that bistability underlies irreversible transitions between low and high Cdk activity states and thereby ensures directionality of cell cycle progression.