The cerebellum, that stripey 'little brain', sits at the back of your head, under your visual cortex, and contains more than half of the neurons in your entire nervous system. The cerebellum is highly conserved across vertebrates, and its evolutionary expansion has tended to proceed in concert with expansion of cerebral cortex. The crystalline neuronal architecture of the cerebellar cortex was first described by Cajal a century ago, and its functional connectivity was elucidated in exquisite anatomical and physiological detail by the mid-20th century. The ability to clearly identify molecularly distinct cerebellar cell types that constitute discrete circuit elements is perhaps unparalleled among brain areas, even within the context of modern circuit neuroscience. Although traditionally thought of as primarily a motor structure, the cerebellum is highly interconnected with diverse brain areas and, as I will explain in this Primer, is well-poised to influence a wide range of motor and cognitive functions.