Most cases of hemiparetic cerebral palsy are caused by perinatal stroke, resulting in lifelong disability for millions of people. However, our understanding of how the motor system develops following such early unilateral brain injury is increasing. Tools such as neuroimaging and brain stimulation are generating informed maps of the unique motor networks that emerge following perinatal stroke. As a focal injury of defined timing in an otherwise healthy brain, perinatal stroke represents an ideal human model of developmental plasticity. Here, we provide an introduction to perinatal stroke epidemiology and outcomes, before reviewing models of developmental plasticity after perinatal stroke. We then examine existing therapeutic approaches, including constraint, bimanual and other occupational therapies, and their potential synergy with non-invasive neurostimulation. We end by discussing the promise of exciting new therapies, including novel neurostimulation, brain-computer interfaces and robotics, all focused on improving outcomes after perinatal stroke.