Recent progress in the comparative analysis of the vertebrate cerebellar organization shows that the cerebella of different tetrapods have a basically similar intrinsic organization, whereas the cerebellum of fishes displays a number of fundamental differences in this respect. Clear examples of teleostean cerebellar specializations are present in the gigantocerebellum of mormyrids, including a valvula cerebelli, the absence of a parasagittal zonal organization, the presence of eurydendroid projection neurons instead of deep cerebellar nuclei, a precerebellar nucleus lateralis valvulae, olivocerebellar fibers that do not climb into the molecular layer, uni- and bilateral locations of granule cells, parallel fibers without a T-shaped bifurcation and with a coextensive distribution in the transverse plane, and different Purkinje cell arrangements including a dendritic palisade pattern. A theoretical exploration of the possible significance of these configurations suggests that they all might be involved in a single main cerebellar function, i.e. coincidence detection of parallel fiber activity by Purkinje cells.