The cerebellar cortex contains the majority of the neurons in the central nervous system, which are well organized in a lattice-like structure. Despite this apparent simplicity, the function of the olivo-cerebellar system is still largely unknown. In this thesis I have tried to contribute to the understanding of the system by studying three aspects of the dynamics of neurons and their relation to the function (see bellow). Although these questions have emerged from the study of the olivo-cerebllar system, the results are more general, and relate to neuronal dynamics and the function of other brain structures.