Movement disorders arise from the complex interplay of multiple changes to neural circuits. Successful treatments for these disorders could interact with these complex changes in myriad ways, and as a consequence their mechanisms of action and their amelioration of symptoms are incompletely understood. Using Parkinson’s disease as a case study, we review here how computational models are a crucial tool for taming this complexity, across causative mechanisms, consequent neural dynamics and treatments. For mechanisms, we review models that capture the effects of losing dopamine on basal ganglia function; for dynamics, we discuss models that have transformed our understanding of how beta-band (15–30 Hz) oscillations arise in the parkinsonian basal ganglia. For treatments, we touch on the breadth of computational modelling work trying to understand the therapeutic actions of deep brain stimulation. Collectively, models from across all levels of description are providing a compelling account of the causes, symptoms and treatments for Parkinson’s disease.