This paper will outline the history of study of the cerebellum from its beginnings to relatively recent times. Although there is no unanimous agreement about what the cerebellum does or how it does it, some principles of its structure and function are well understood. The historical approach can help to identify remaining questions and point the way to future progress. We make no effort to separate anatomical, physiological and clinical studies; rather, we hope to emphasize their interrelation. The cerebellum has always been seen as a distinct subdivision of the brain. Over the years there was an increasingly accurate description of its gross appearance and major subdivisions. By the beginning of the 19th century, the classical descriptive anatomical work was completed, and experimental study of the functions of the cerebellum began. Lesions were made in the cerebellum of experimental animals, and the behavioral deficits that were caused by the lesion were studied and described. These early animal studies powerfully influenced clinical interpretation of the symptoms seen in patients with cerebellar disease. Several questions are implicit in the anatomical and clinical studies of the nineteenth and early twentieth centuries, some of which remain incompletely answered. Many of these are addressed in other chapters in this volume. 1. Do different parts of the cerebellum do different things? The uniformity of the neuronal architecture of the cerebellar cortex suggests that each small region must operate in a similar way, but it is also clear that different regions control different functions. Is there a systematic sensory and/or body representation? 2. What are the functions of the cerebellar hemispheres? Massive in humans and very large in primates, their functions remain in dispute. Because the size of the cerebellar hemispheres parallels the development of the cerebral cortex, some have suggested that the hemispheres in humans and the higher primates may play a role in cognitive functions. 3. If one part of the cerebellum is damaged, can another part take over? A related question is whether normal motor function is possible in cases of complete or near-complete agenesis of the cerebellum. 4. What are the functions of the two distinctly different afferent systems to the cerebellum; the climbing and mossy fibers?