The cerebellum is one of the best studied parts of the brain. Its three-layered cortex and well-defined afferent and efferent fibre connections make the cerebellum a favourite field for research on the connectivity of the brain. The cerebellar cortex is composed of four main types of neurons: granule cells, Purkinje cells and two types of inhibitory interneurons, the Golgi cells and the stellate or basket cells. The cerebellar cortex receives three kinds of inputs: the mossy fibres (most afferent systems), the climbing fibres from the inferior olive and diffusely organized monoaminergic and cholinergic fibres. The general idea that the cerebellum functions to regulate muscle tone and coordinate movements arose from experiments in the nineteenth century. The cerebellum plays a role not only in motor control but also in motor learning and cognition. Cerebellar disorders typically manifest themselves by ataxia which is characterized by incoordination of balance, instability of gait, extremity and eye movements and dysarthria. More recently, it has become apparent that cerebellar lesions do not always lead to ataxic motor symptoms. The cerebellar cognitive affective syndrome includes impairments in executive, visuospatial and linguistic abilities, with affective disturbance ranging from emotional blunting and depression to disinhibition and psychotic features. Following a few notes on the development of the cerebellum (Sect. 10.2), gross morphology and subdivision (Sect. 10.3), cerebellar circuitry (Sect. 10.4), the cerebellar nuclei (Sect. 10.5), the cerebellar peduncles (Sect. 10.6) and the precerebellar nuclei (Sect. 10.7), cerebellar afferent connections (Sect. 10.8), cerebellar output (Sect. 10.9) and cerebellar dysfunction (Sect. 10.9) will be discussed. Pathophysiological aspects of ataxia are discussed in Sect. 10.11 and the cerebellar cognitive affective syndrome in Sect. 10.12. The role of the cerebellum in motor control and cognition is illustrated in several Clinical cases. The English terms of the Terminologia Neuroanatomica are used throughout.