For many decades, the predominant view in the cerebellar field has been that the olivocerebellar system's primary function is to induce plasticity in the cerebellar cortex, specifically, at the parallel fiber-Purkinje cell synapse. However, it has also long been proposed that the olivocerebellar system participates directly in motor control by helping to shape ongoing motor commands being issued by the cerebellum. Evidence consistent with both hypotheses exists; however, they are often investigated as mutually exclusive alternatives. In contrast, here, we take the perspective that the olivocerebellar system can contribute to both the motor learning and motor control functions of the cerebellum and might also play a role in development. We then consider the potential problems and benefits of it having multiple functions. Moreover, we discuss how its distinctive characteristics (e.g., low firing rates, synchronization, and variable complex spike waveforms) make it more or less suitable for one or the other of these functions, and why having multiple functions makes sense from an evolutionary perspective. We did not attempt to reach a consensus on the specific role(s) the olivocerebellar system plays in different types of movements, as that will ultimately be determined experimentally; however, collectively, the various contributions highlight the flexibility of the olivocerebellar system, and thereby suggest that it has the potential to act in both the motor learning and motor control functions of the cerebellum.