The functional capacity of the human lung as gas exchanger is to a large extent determined by structural design. Quantitative structure-function correlations can be established by morphometry. A very large surface of air-blood contact, together with a very thin tissue barrier, are required to permit adequate oxygen uptake under work conditions. However, these design features also pose problems, such as how to ventilate and perfuse this large surface evenly and efficiently, or how to ensure mechanical stability against surface forces with a minimum of supporting tissue. The discussion focuses on the extent to which novel design principles are used to overcome such problems by designing the airways as a fractal tree and the fibre support system as a tensegrity structure.