There is an urgent need to understand how SARS-CoV-2 infects the airway epithelium and in a subset of individuals leads to severe illness or death. Induced pluripotent stem cells (iPSCs) provide a near limitless supply of human cells that can be differentiated into cell types of interest, including airway epithelium, for disease modeling. We present a human iPSC-derived airway epithelial platform, composed of the major airway epithelial cell types, that is permissive to SARS-CoV-2 infection. Subsets of iPSC-airway cells express the SARS-CoV-2 entry factors angiotensin-converting enzyme 2 ( ACE2), and transmembrane protease serine 2 ( TMPRSS2). Multiciliated cells are the primary initial target of SARS-CoV-2 infection. On infection with SARS-CoV-2, iPSC-airway cells generate robust interferon and inflammatory responses, and treatment with remdesivir or camostat mesylate causes a decrease in viral propagation and entry, respectively. In conclusion, iPSC-derived airway cells provide a physiologically relevant in vitro model system to interrogate the pathogenesis of, and develop treatment strategies for, COVID-19 pneumonia.