Recapitulation of lung development from human pluripotent stem cells (hPSCs) in three dimensions (3D) would allow deeper insight into human development, as well as the development of innovative strategies for disease modelling, drug discovery and regenerative medicine. We report here the generation from hPSCs of lung bud organoids (LBOs) that contain mesoderm and pulmonary endoderm and develop into branching airway and early alveolar structures after xenotransplantation and in Matrigel 3D culture. Expression analysis and structural features indicated that the branching structures reached the second trimester of human gestation. Infection in vitro with respiratory syncytial virus, which causes small airway obstruction and bronchiolitis in infants, led to swelling, detachment and shedding of infected cells into the organoid lumens, similar to what has been observed in human lungs. Introduction of mutation in HPS1, which causes an early-onset form of intractable pulmonary fibrosis, led to accumulation of extracellular matrix and mesenchymal cells, suggesting the potential use of this model to recapitulate fibrotic lung disease in vitro. LBOs therefore recapitulate lung development and may provide a useful tool to model lung disease.