Regulated transport of the plant hormone auxin is central to many aspects of plant development. Directional transport, mediated by membrane transporters, produces patterns of auxin distribution in tissues that trigger developmental processes, such as vascular patterning or leaf formation. Experimentation has produced many, largely qualitative, data providing strong evidence for multiple feedback systems between auxin and its transport. However, the exact mechanisms concerned remain elusive and the experiments required to evaluate alternative hypotheses are challenging. Because of this, computational modelling now plays an important role in auxin transport research. Here we review some current approaches and underlying assumptions of computational auxin transport models. We focus on self-organising models for polar auxin transport and on recent attempts to unify conflicting mechanistic explanations. In addition, we discuss in general how these computer simulations are proving to be increasingly effective in hypothesis generation and testing, and how simulation can be used to direct future experiments.Editor's suggested further reading in BioEssays Local auxin production: a small contribution to a big field Abstract.