The perceptron has served as a prototypical neuronal learning machine in the physics community interested in neural networks and artificial intelligence, which included Gérard Toulouse as one of its prominent figures. It has also been used as a model of Purkinje cells of the cerebellum, a brain structure involved in motor learning, in the early influential theories of David Marr and James Albus. We review these theories, more recent developments in the field, and highlight questions of current interest.