The central assumption of existing models of motor learning in the cerebellum is that cerebellar mossy fibres signal information about the context in which a movement is to be performed and climbing fibres signal in relation to a movement error. This leads to changes in the responsiveness of Purkinje cells, which on the next occasion will generate a corrected output in a given context. Support for this view has come mainly from work on adaptation of the vestibulo-ocular reflex. The discovery that classically conditioned eyeblink responses depend critically on the cerebellum offers the possibility to study the learning of a novel behaviour, rather than modification of an existing reflex. After repeated pairing of a neutral stimulus, such as a tone, with a blink-eliciting stimulus, the tone will acquire the ability to elicit a blink on its own. We review evidence from studies employing a wide variety of techniques that the cerebellum is critical in this type of learning as well as evidence that mossy and climbing fibres have roles assigned to them in cerebellar learning models.