Some of the events of the cell cycle appear to be triggered by a bistable mechanism. A bistable biochemical system can respond to a small, slow signal and is carried by positive feedback from one stable steady state directly to another, in an all-or-none manner. Slow or subthreshold stimuli do not cause accommodation or loss of excitability. Switching is not readily reversible by removing the stimulus, i.e. there is hysteresis: reversal generally requires a stronger, opposite stimulus. Biochemically, bistable biochemical switching requires positive feedback, and mechanisms for stabilizing the system against premature activation and for destabilization in response to a biological signal. Three bistable biochemical models, all suggested by reported experimental observations, are described and analysed. These models suggest that a titratable inhibitor may play an important part in bistable switching, because the end-point of titration can form a natural threshold for enhancement of positive feedback.