Branched structures are evident at all levels of organization in living organisms. Many organs, such as the vascular system, lung, kidney and mammary gland, are heavily branched. In each of these cases, equally fascinating questions have been put forward, including those that address the cellular and molecular mechanisms that regulate the branching process itself, such as where the branches are initiated and how they extend and grow in the right direction. Recent experiments suggest that cell competition and cell rearrangements might be conserved key features in branch formation and might be controlled by local cell signalling.