Alterations in neuronal connectivity, particularly in the “peri-infarct” tissue adjacent to the region of ischemic damage, are important contributors to the spontaneous recovery of function that commonly follows stroke. Peri-infarct astrocytes undergo reactive astrogliosis and play key roles in modulating the adaptive responses in neurons. This reactive astrogliosis shares many features with that induced by other forms of damage to the central nervous system but also differs in details that potentially influence neurological recovery. A subpopulation of astrocytes within a few hundred micrometers of the infarct proliferate and are centrally involved in the development of the glial scar that separates the damaged tissue in the infarct from surrounding normal brain. The intertwined processes of astrocytes adjacent to the infarct provide the core structural component of the mature scar. Interventions that cause early disruption of glial scar formation typically impede restoration of neurological function. Marked reactive astrogliosis also develops in cells more distant from the infarct but these cells largely remain in the spatial territories they occupied prior to stroke. These cells play important roles in controlling the extracellular environment and release proteins and other molecules that are able to promote neuronal plasticity and improve functional recovery. Treatments manipulating aspects of reactive astrogliosis can enhance neuronal plasticity following stroke. Optimising these treatments for use in human stroke would benefit from a more complete characterization of the specific responses of peri-infarct astrocytes to stroke as well as a better understanding of the influence of other factors including age, sex, comorbidities and reperfusion of the ischemic tissue.