Pathologies of the respiratory system such as lung infections, chronic inflammatory lung diseases, and lung cancer are among the leading causes of morbidity and mortality, killing one in six people worldwide. Development of more effective treatments is hindered by the lack of preclinical models of the human lung that can capture the disease complexity, highly heterogeneous disease phenotypes, and pharmacokinetics and pharmacodynamics observed in patients. The merger of two novel technologies, Organs-on-Chips and human stem cell engineering, has the potential to deliver such urgently needed models. Organs-on-Chips, which are microengineered bioinspired tissue systems, recapitulate the mechanochemical environment and physiological functions of human organs while concurrent advances in generating and differentiating human stem cells promise a renewable supply of patient-specific cells for personalized and precision medicine. Here, we discuss the challenges of modeling human lung pathophysiology in vitro, evaluate past and current models including Organs-on-Chips, review the current status of lung tissue modeling using human pluripotent stem cells, explore in depth how stem-cell based Lung-on-Chips may advance disease modeling and drug testing, and summarize practical consideration for the design of Lung-on-Chips for academic and industry applications.