Humans are highly social animals whose survival and well-being depend on their capacity to cooperate in complex social settings. Advances in anthropology and psychology have demonstrated the importance of cooperation for enhancing social cohesion and minimizing conflict. The understanding of social behavior is informed by the notion of social cognition, a set of mental operations including emotion perception, mentalizing, and empathy. The social brain hypothesis posits that the mammalian brain has enlarged over evolution to meet the challenges of social life, culminating in a large human brain well adapted for social cognition. The structures subserving social cognition are mainly located in the frontal and temporal lobes, and although gray matter is critical, social cognition also requires white matter. Whereas the social brain hypothesis assumes that brain enlargement has been driven by neocortical expansion, cerebral white matter has expanded even more robustly than the neocortex, coinciding with the emergence of social cognition. White matter expansion is most evident in the frontal and temporal lobes, where it enhances connectivity between regions critical for social cognition. Myelination has, in turn, conferred adaptive social advantages by enabling prompt empathic concern for offspring and by strengthening networks that support cooperation and the related capacities of altruism and morality. Social cognition deficits related to myelinated tract involvement occur in many disorders, including stroke, Binswanger disease, traumatic brain injury, multiple sclerosis, glioma, and behavioral variant frontotemporal dementia. The contribution of white matter to social cognition can be conceptualized as the enhancement of cooperation through brain connectivity.