We present a new hypothesis of cerebellar function that is based on synchronization, delayed reverberation, and time windows for triggering spikes. Our model suggests that granule cells admit mossy fiber activity to the parallel fibers only if the Golgi cells are firing synchronously and if the mossy-fiber spikes arrive within short and well-defined time windows. The concept of time window control organizes neuronal activity in discrete 'time slices' that can be used to discern meaningful information from background noise. In particular, Purkinje cell activity can trigger rebound spikes in deep cerebellar nuclei cells, which project via brain stem nuclei and mossy fibers back to the cerebellar cortex. Using a detailed model of deep cerebellar nuclei cells, we demonstrate that the delayed firing of rebound spikes is a robust mechanism so as to ensure that the reverberated activity re-arrives in the mossy fibers just during the granule-cell time window. Large network simulations reveal that synaptic plasticity (LTD and LTP) at the parallel fiber/Purkinje cell synapses that relies on the timing of the parallel fiber and climbing fiber activities allows the system to learn, store, and recall spatiotemporal patterns of spike activity. Climbing fiber spikes function both as teacher and as synchronization signals. The temporal characteristics of the climbing fiber activity are due to intrinsic oscillatory properties of inferior olivary neurons and to reverberating projections between deep cerebellar nuclei, the mesodiencephalic junction, and the inferior olive. Thus, the reverberating loops of the mossy fiber system and climbing fiber system may interact directly with the time windows provided by the circuitry of the cerebellar cortex so as to generate the appropriate spatio-temporal firing patterns in the deep cerebellar nuclei neurons that control premotor systems. In future studies the model will be extended in that high frequency simple spike activities will be included and that their relevance for motor control will be addressed.