Tissue engineering and in vitro modeling of the airways and lungs in the respiratory system are of substantial research and clinical importance. In vitro airway and lung models aim to improve treatment options for airway and lung repair and advance respiratory pathophysiological research. The construction of biomimetic native airways and lungs with tissue-specific biological, mechanical, and configurable features remains challenging. Bioprinting, an emerging 3D printing technology, is promising for the development of airway, lung, and disease models, allowing the incorporation of cells and biologically active molecules into printed constructs in a precise and reproducible manner to recreate the airways, lung architecture, and in vitro microenvironment. Herein, we present a review of airway and lung bioprinting for applications in tissue engineering and in vitro modeling. The key pathophysiological characteristics of the airway, lung interstitium, and alveoli are described. The bioinks recently used in 3D bioprinting of the airways and lungs are summarized. Furthermore, we propose a bioink categorization based on the structural characteristics of the lungs and airways. Finally, the challenges and opportunities in the research on biofabrication of airways and lungs are discussed.