Branched structures appear in a myriad of contexts in biological systems, fulfilling numerous functions. The bronchial airway is one of the most famous examples. Its architecture has long fascinated both biologists and theoreticians due to its complexity and regularity. It can be understood as a fractal-like design, which has evolved as a solution to the problem of simultaneously maximising surface area and optimising fluid transport efficiency. One of the most intriguing questions that arises is how such an intricate structure is achieved robustly during development. While much progress has been made in uncovering the biochemical pathways involved in the regulation of lung branching morphogenesis, it remains unclear how the global network structure emerges from the interactions of thousands of growing branches. In this talk, I will present our recent work in formulating a statistical framework for understanding the dynamics of the developing human bronchial airway. By studying organ-scale images of human foetal lungs throughout development, we are able to map the organisation of the growing network in 3D. Combining computational morphometric and network analysis, we deduce a minimal model that shows how the network structure can be understood to emerge in a self-organised manner from simple, local branching rules.