Lung alveoli, which are unique to air-breathing organisms, have been challenging to generate from pluripotent stem cells (PSCs) in part because there are limited model systems available to provide the necessary developmental roadmaps for in vitro differentiation. Here we report the generation of alveolar epithelial type 2 cells (AEC2s), the facultative progenitors of lung alveoli, from human PSCs. Using multicolored fluorescent reporter lines, we track and purify human SFTPC+ alveolar progenitors as they emerge from endodermal precursors in response to stimulation of Wnt and FGF signaling. Purified PSC-derived SFTPC+ cells form monolayered epithelial "alveolospheres" in 3D cultures without the need for mesenchymal support, exhibit self-renewal capacity, and display additional AEC2 functional capacities. Footprint-free CRISPR-based gene correction of PSCs derived from patients carrying a homozygous surfactant mutation (SFTPB^121ins2) restores surfactant processing in AEC2s. Thus, PSC-derived AEC2s provide a platform for disease modeling and future functional regeneration of the distal lung.