Synaesthesia is a heritable condition of involuntary sensory cross-activation whereby the presentation of a particular stimulus elicits a secondary sensory-perceptual experience. It is thought to be caused by aberrant cross-activation of one cortical area by another, but models differ as to whether this reflects functional or structural differences in the brains of synaesthetes. Here we consider these models in light of recent experimental findings and argue for structural differences in the brains of synaesthetes, which might be more widespread than expected. We also discuss several plausible developmental mechanisms that could link a putative genetic variant to altered cortical connectivity and illustrate how synaesthesia could be an informative model to investigate how patterns of connectivity between cortical areas are established.