Elastic fibres are a major class of extracellular matrix fibres that are abundant in dynamic connective tissues such as arteries, lungs, skin and ligaments. Their structural role is to endow tissues with elastic recoil and resilience. They also act as an important adhesion template for cells, and they regulate growth factor availability. Mutations in major structural components of elastic fibres, especially elastin, fibrillins and fibulin-5, cause severe, often life-threatening, heritable connective tissue diseases such as Marfan syndrome, supravalvular aortic stenosis and cutis laxa. Elastic-fibre function is also frequently compromised in damaged or aged elastic tissues. The ability to regenerate or engineer elastic fibres and tissues remains a significant challenge, requiring improved understanding of the molecular and cellular basis of elastic-fibre biology and pathology, and ability to regulate the spatiotemporal expression and assembly of its molecular components.