The cerebellum is well developed in cartilaginous fishes, with the same cell types (barring basket cells) 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 fibers, interneurons, spiny Purkinje cell dendrites, and climbing fibers) is a defining characteristic. In addition to the cerebellum, cartilaginous fishes have cerebellum-like structures in the dorsolateral wall of the hindbrain. These structures are adjacent to and, in part, contiguous with the cerebellum. They are cerebellum-like in that they have a molecular layer of parallel fibers and inhibitory interneurons that has striking organizational similarities to the molecular layer of the cerebellar cortex. However, these structures also have characteristics that differ from the cerebellum. For example, cerebellum-like structures do not have climbing fibers and 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 of researchers to characterize signal processing in these structures in a behaviorally relevant context, good progress has been made in determining the fundamental processing algorithm of the cerebellum-like structures. This algorithm enables the molecular layer to act as an adaptive filter that cancels self-generated noise in electrosensory and lateral line systems. Given the fundamental similarities of the molecular layer across these structures and the phylogeny of these structures across basal vertebrates, it is clear that these structures share a common genetic-developmental program. Syngeny is a term that has been used to describe similarity of structure due to a shared genetic-developmental program, whether the structures are phylogenetically homologous or not. Given that the cerebellum and cerebellum-like structures are physically adjacent, we propose that cerebellum-like structures were the evolutionary antecedent of the cerebellum and that the cerebellum arose through a change in the genetic-developmental program, amounting to a duplication of existing structure. Such duplication to form adjacent structures can be considered a special case of syngeny. On this view, the cerebellum is an evolutionary innovation in gnathostomes that is literally superimposed on pre-existing underlying brain structures and pathways. From this perspective, the cerebellum can be considered an example of 'subsumption architecture', a term that describes the addition of modules that add computational power while maintaining existing fundamental functionality. This addition is reflected in the finding that in elasmobranchs with relatively large brains, the size of the telencephalon and cerebellum enlarge disproportionately, while those parts of the brain that contain more direct sensory and motor connections do not. Added 'computational' power in the chondrichthyan brain and the comparative function and evolution of the cerebellum and cerebellum-like structures across the cartilaginous fishes supports the idea of the cerebellum as an example of subsumption architecture.