Many organs including the mammalian lung and vascular system consist of branched tubular networks that transport essential gases or fluids, but the genetic programs that control the development of these complex three-dimensional structures are not well understood. The Drosophila melanogaster tracheal (respiratory) system is a network of interconnected epithelial tubes that transports oxygen and other gases in the body and provides a paradigm of branching morphogenesis. It develops by sequential sprouting of primary, secondary, and terminal branches from an epithelial sac of approximately 80 cells in each body segment of the embryo. Mapping of the cell movements and shape changes during the sprouting process has revealed that distinct mechanisms of epithelial migration and tube formation are used at each stage of branching. Genetic dissection of the process has identified a general program in which a fibroblast growth factor (FGF) and fibroblast growth factor receptor (FGFR) are used repeatedly to control branch budding and outgrowth. At each stage of branching, the mechanisms controlling FGF expression and the downstream signal transduction pathway change, altering the pattern and structure of the branches that form. During terminal branching, FGF expression is regulated by hypoxia, ensuring that tracheal structure matches cellular oxygen need. A branch diversification program operates in parallel to the general budding program: Regional signals locally modify the general program, conferring specific structural features and other properties on individual branches, such as their substrate outgrowth preferences, differences in tube size and shape, and the ability to fuse to other branches to interconnect the network.