This review describes the subjective experience of visual aura in migraine, outlines theoretical models of this phenomenon, and explores how these may be linked to neurochemical, electrophysiological and psychophysical differences in sensory processing that have been reported in migraine with aura. Reaction-diffusion models have been used to model the hallucinations thought to arise from cortical spreading depolarisation and depression in migraine aura. One aim of this review is to make the underlying principles of these models accessible to a general readership. Cortical spreading depolarisation and depression in these models depends on the balance of the diffusion rate between excitation and inhibition, and the occurrence of a large spike in activity to initiate spontaneous pattern formation. We review experimental evidence, including recordings of brain activity made during the aura and attack phase, self-reported triggers of migraine, and psychophysical studies of visual processing in migraine with aura, and how these might relate to mechanisms of excitability that make some people susceptible to aura. Increased cortical excitability, increased neural noise, and fluctuations in oscillatory activity across the migraine cycle are all factors likely to contribute to the occurrence of migraine aura. There remain many outstanding questions relating to the current limitations of both models and experimental evidence. Nevertheless, reaction-diffusion models, by providing an integrative theoretical framework, support the generation of testable experimental hypotheses to guide future research.