Synaesthesia is a phenomenon in which stimulation in one sensory modality triggers involuntary experiences typically not associated with that stimulation. Inducing stimuli (inducers) and synaesthetic experiences (concurrents) may occur within the same modality (e.g., seeing colours while reading achromatic text) or span across different modalities (e.g., tasting flavours while listening to music). Although there has been considerable progress over the last decade in understanding the cognitive and neural mechanisms of synaesthesia, the focus of current neurocognitive models of synaesthesia does not encompass many crucial psychophysical characteristics documented in behavioural research. Prominent theories of the neurophysiological basis of synaesthesia construe it as a perceptual phenomenon and hence focus primarily on the modality-specific brain regions for perception. Many behavioural studies, however, suggest an essential role for conceptual-level information in synaesthesia. For example, there is evidence that synaesthetic experience arises subsequent to identification of an inducing stimulus, differs substantially from real perceptual events, can be akin to perceptual memory, and is susceptible to lexical/semantic contexts. These data suggest that neural mechanisms lying beyond the realm of the perceptual cortex (especially the visual system), such as regions subserving conceptual knowledge, may play pivotal roles in the neural architecture of synaesthesia. Here we discuss the significance of non-perceptual mechanisms that call for a re-evaluation of the emphasis on synaesthesia as a perceptual phenomenon. We also review recent studies which hint that some aspects of synaesthesia resemble our general conceptual knowledge for object attributes, at both psychophysical and neural level. We then present a conceptual-mediation model of synaesthesia in which the inducer and concurrent are linked within a conceptual-level representation. This ‘inducer-to-concurrent’ n