The structure of the cerebellar cortex is remarkably similar across vertebrate phylogeny. It is well developed in basal jawed fishes, such as sharks and rays with many of the same cell types and organizational features found in other vertebrate groups, including mammals. In particular, the lattice-like organization of cerebellar cortex (with a molecular layer of parallel fibres, interneurons, spiny Purkinje cell dendrites, and climbing fires) is a common defining characteristic. In addition to the cerebellar cortex, fishes and aquatic amphibians have a variety of cerebellum-like structures in the dorso-lateral wall of the hindbrain. These structures are adjacent to, and in part, contiguous with, the cerebellum. They derive their cerebellum-like name from the presence of a molecular layer of parallel fibers and inhibitory interneurons, which has striking organizational similarities to the molecular layer of the cerebellar cortex. However, these structures also have characteristics which differ from the cerebellum. For example, cerebellum-like structures do not have climbing fibres, and they are clearly sensory. They receive direct afferent input from peripheral sensory receptors and relay their outputs to midbrain sensory areas. As a consequence of this close sensory association, and the ability to characterise their signal processing in a behaviourally relevant context, good progress has been made in determining the fundamental processing algorithm in cerebellar-like structures. In particular, we have come to understand the contribution to signal processing made by the molecular layer, which provides an adaptive filter to cancel self-generated noise in electrosensory and lateral line systems. Given the fundamental similarities of the molecular layer across these structures, coupled with evidence that cerebellum-like structures may have been the evolutionary antecedent of the cerebellum, we address the question: do both share the same functional algorithm?