The primary function of the lung is to supply the body with oxygen and eliminate carbon dioxide during breathing. To achieve this, the mammalian lung has evolved a complex bifurcating airway tree embedded in the parenchyma, comprised of alveoli, alveolar ducts and capillaries. The mechanical properties of the alveoli determine how easily the lung can be inflated. The overall stiffness of the parenchyma is an emergent property arising from the nature of its components and the way they are organized. The stiffness of individual alveoli is primarily determined by its load-bearing components, the collagen and elastic fibers. The other major contributor to stiffness is the surface tension at the interface between the air in the lungs and the fluid that lines the alveoli. The forces involved in the cyclic stretching of the tissue during breathing are sensed by resident lung cells that respond so as to maintain and repair the lung in the face of ongoing wear and tear as well as environmental exposures. Lung biology and mechanics are thus tightly coupled, with crucial implications for development, homeostasis, and response to injury and disease. The possibilities for investigating this rich functional and structural landscape through computational modeling are limitless.