Auxin interacts with its own polar transport to influence cell polarity and tissue patterning. Research over the past decade has started to deliver new insights into the molecular mechanisms that drive and regulate polar auxin transport. The most prominent auxin efflux protein, PIN1, has subsequently become a crucial component of auxin transport models because it is now known to direct auxin flow and maintain local auxin gradients. Recent molecular and genetic experiments have allowed the formulation of conceptual models that are able to interpret the role of (i) auxin, (ii) its transport, and (iii) the dynamics of PIN1 in generating temporal and spatial patterns. Here we review the current mathematical models of patterning in two specific developmental contexts: lateral shoot and vein formation, focusing on how these models can help to untangle the details of auxin transport-mediated patterning.