The reorganization of epithelial sheets into tubes is a fundamental process in the formation of many organs, such as the lungs, kidneys, gut, and neural tube. This process involves the patterning of distinct cell types and the coordination of those cells during the shape changes and rearrangements that produce the tube. A better understanding of the cellular and genetic mechanisms that regulate tube formation is necessary for tissue engineers to develop functional organs in vitro. The Drosophila egg chamber has emerged as an outstanding model for studying tubulogenesis. Synthesis of the dorsal respiratory appendages by the follicular epithelium resembles primary neurulation in vertebrates. This review summarizes work on the patterning and morphogenesis of the dorsal-appendage tubes and highlights key areas where mathematical modeling could contribute to our understanding of these processes.