Stroke is a common problem, and with an aging population, it is likely to become more so. Outcomes from stroke are wide ranging from death to complete recovery, but the majority result in severe motor impairments that affect quality of life and become a burden on health care systems, family, and friends. Therapeutically, removal of thromboses can greatly improve outcomes, but for many stroke sufferers, the only currently available therapy is rehabilitative training in which spared brain areas and fiber tracts are strengthened and trained to take over new functions. Experimental data in animals show that this is in part based on changes in the connectivity of the brain and spinal cord and on the growth of new nerve fiber branches, a process called structural plasticity. So, just how plastic is the brain after a stroke? In this review, we explore the factors that affect plasticity after strokes, such as age and the overall size and location of the lesion. We discuss the peri-infarct area as extensive research has shown that processes occurring there are likely to be involved mechanistically in plastic changes in cortical circuitry. Finally, we review promising interventions being tested preclinically and discuss those that have been translated into clinical research.