The mechanism by which a learnt synaptic weight change can contribute to learning or adaptation of brain function is a type of credit assignment problem, which is a key issue for many parts of the brain. In the cerebellum, detailed knowledge not only of the local circuitry connectivity but also of the topography of different sources of afferent/external information makes this problem particularly tractable. In addition, multiple forms of synaptic plasticity and their general rules of induction have been identified. In this review, we will discuss the possible roles of synaptic and cellular plasticity at specific locations in contributing to behavioral changes. Focus will be on the parts of the cerebellum that are devoted to limb control, which constitute a large proportion of the cortex and where the knowledge of the external connectivity is particularly well known. From this perspective, a number of sites of synaptic plasticity appear to primarily have the function of balancing the overall level of activity in the cerebellar circuitry, whereas the locations at which synaptic plasticity leads to functional changes in terms of limb control are more limited. Specifically, the postsynaptic forms of long-term potentiation (LTP) and long-term depression (LTD) at the parallel fiber synapses made on interneurons and Purkinje cells, respectively, are the types of plasticity that mediate the widest associative capacity and the tightest link between the synaptic change and the external functions that are to be controlled.