Brain structure varies between people in a markedly organized fashion. Communities of brain regions co-vary in their morphological properties. For example, cortical thickness in one region influences the thickness of structurally and functionally connected regions. Such networks of structural co-variance partially recapitulate the functional networks of healthy individuals and the foci of grey matter loss in neurodegenerative disease. This architecture is genetically heritable, is associated with behavioural and cognitive abilities and is changed systematically across the lifespan. The biological meaning of this structural co-variance remains controversial, but it appears to reflect developmental coordination or synchronized maturation between areas of the brain. This Review discusses the state of current research into brain structural co-variance, its underlying mechanisms and its potential value in the understanding of various neurological and psychiatric conditions.