With the advent of rodent models of l-DOPA-induced dyskinesia (LID), a growing literature has linked molecular changes in the striatum to the development and expression of abnormal involuntary movements. Changes in information processing at the striatal level are assumed to impact on the activity of downstream basal ganglia nuclei, which in turn influence brain-wide networks, but very little is actually known about systems-level mechanisms of dyskinesia. As an aid to approach this topic, we here review the anatomical and physiological organisation of cortico-basal ganglia-thalamocortical circuits, and the changes affecting these circuits in animal models of parkinsonism and LID. We then review recent findings indicating that an abnormal cerebellar compensation plays a causal role in LID, and that structures outside of the classical motor circuits are implicated too. In summarizing the available data, we also propose hypotheses and identify important knowledge gaps worthy of further investigation. In addition to informing novel therapeutic approaches, the study of LID can provide new clues about the interplay between different brain circuits in the control of movement.