Polar auxin transport intimately connects plant cell polarity and multicellular patterning. Through the transport of the small molecule indole-3-acetic acid, plant cells integrate their polarities and communicate the degree of their polarization. In this way, they generate an apical-basal axis that serves as a positional reference anchoring subsequent patterning events. Research in recent years has brought the molecular mechanisms underlying auxin perception and auxin transport to light. This knowledge has been used to derive spectacular molecular visualization tools and animated computer simulations, which are now allied in a joint systems biology effort towards a mathematical description of auxin-transport-mediated patterning processes.