<p>The rise of the deep neural network as the workhorse of artificial intelligence has brought increased attention to how network architectures serve specialized functions. The cerebellum, with its largely shallow, feedforward architecture, provides a curious example of such a specialized network. Within the cerebellum, tiny supernumerary granule cells project to a monolayer of giant Purkinje neurons that reweight synaptic inputs under the instructive influence of a unitary synaptic input from climbing fibres. What might this predominantly feedforward organization confer computationally? Here we review evidence for and against the hypothesis that the cerebellum learns basic associative feedforward control policies to speed up motor control and learning. We contrast and link this feedforward control framework with another prominent set of theories proposing that the cerebellum computes internal models. Ultimately, we suggest that the cerebellum may implement control through mechanisms that resemble internal models but involve model-free implicit mappings of high-dimensional sensorimotor contexts to motor output.</p>