During its lifetime, the mammary gland undergoes many phases of development and differentiation. Much of this occurs during puberty, when the ductal epithelium expands by branching morphogenesis, invading the surrounding fat pad to form an organised mammary tree. Throughout its existence, the epithelium will go through several cycles of proliferation and cell death during pregnancy, lactation and involution. Many of the signalling mechanisms which control the initial invasion of the fat pad by the epithelium, and regulate its continuing plasticity, can be harnessed or corrupted by tumour cells in order to support their aberrant growth and progression towards invasion. This is true not just for the epithelial cells themselves but also for cells in the surrounding microenvironment, including fibroblasts, macrophages and adipocytes. This review examines the complex web of signalling and adhesion interactions controlling branching morphogenesis, and how their alteration can promote malignancy. Current in vivo and in vitro mammary gland models are also discussed. (Part of a Multi-author Review).