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Over the past 30 years, cumulative evidence has indicated that cerebellar function extends beyond sensorimotor control. This view has emerged from studies of neuroanatomy, neuroimaging, neuropsychology, and brain stimulation, with the results implicating the cerebellum in domains as diverse as attention, language, executive function, and social cognition. Although the literature provides sophisticated models of how the cerebellum helps refine movements, it remains unclear how the core mechanisms of these models can be applied when considering a broader conceptualization of cerebellar function. In light of recent multidisciplinary findings, we examine how two key concepts that have been suggested as general computational principles of cerebellar function- prediction and error-based learning- might be relevant in the operation of cognitive cerebro-cerebellar loops.