The emergence of tissue engineering raises new possibilities for the study of complex physiological and pathophysiological processes in vitro. Many tools are now available to create 3D tissue models in vitro, but the blueprints for what to make have been slower to arrive. We discuss here some of the 'design principles' for recreating the interwoven set of biochemical and mechanical cues in the cellular microenvironment, and the methods for implementing them. We emphasize applications that involve epithelial tissues for which 3D models could explain mechanisms of disease or aid in drug development.