Tissues arising late in evolutionary time, such as lung alveoli that are unique to air breathing organisms, have been challenging to generate in vitro from pluripotent stem cells (PSCs), in part because there are limited lower organism model systems available to provide the necessary developmental roadmaps to guide in vitro differentiation. Furthermore, pulmonary alveolar epithelial type II cell (AEC2) dysfunction has been implicated as a primary cause of pathogenesis in many poorly understood lung diseases that lack effective therapies, including interstitial lung disease (ILD) and emphysema. Here we report the successful directed differentiation in vitro of human PSCs into AEC2s, the facultative progenitors of lung alveoli. Using gene editing to engineer multicolored fluorescent reporter PSC lines (NKX2-1GFP;SFTPCtdTomato), we track and purify human SFTPC+ alveolar progenitors as they emerge from NKX2-1+ endodermal developmental precursors in response to stimulation of Wnt and FGF signaling. Purified PSC-derived SFTPC+ cells are able to form monolayered epithelial spheres (“alveolospheres”) in 3D cultures without the need for mesenchymal co-culture support, exhibit extensive self-renewal capacity, and display additional canonical AEC2 functional capacities, including innate immune responsiveness, the production of lamellar bodies able to package surfactant, and the ability to undergo squamous cell differentiation while upregulating type 1 alveolar cell markers. Guided by time-series global transcriptomic profiling we find that AEC2 maturation involves downregulation of Wnt signaling activity, and the highest differentially expressed transcripts in the resulting SFTPC+ cells encode genes associated with lamellar body and surfactant biogenesis. Finally, we apply this novel model system to generate patient-specific AEC2s from induced PSCs (iPSCs) carrying homozygous surfactant mutations (SFTPB121ins2), and we employ footprint-free CRISPR-based gene editing to observe that correction of this genetic lesion restores surfactant processing in the cells responsible for their disease. Thus we provide an approach for disease modeling and future functional regeneration of a cell type unique to air-breathing organisms.