Recent years have seen rapid progress in our understanding of the mechanism of action of the plant hormone auxin. A major emerging theme is the central importance of the interplay between auxin signalling and the active transport of auxin through the plant to create dynamic patterns of auxin accumulation. Even in tissues where auxin distribution patterns appear stable, they are the product of standing waves, with auxin flowing through the tissue, maintaining local pockets of high and low concentration. The auxin distribution patterns result in changes in gene expression to trigger diverse, context-dependent growth and differentiation responses. Multi-level feedback loops between the signal transduction network and the auxin transport network provide self-stabilising patterns that remain sensitive to the external environment and to the developmental progression of the plant. The full biological implications of the behaviour of this system are only just beginning to be understood through a combination of experimental manipulation and mathematical modelling.