An enduring question in cognitive neuroscience is how the physical properties of the world are represented in the brain to yield conscious perception. In most people, a particular physical stimulus gives rise to a unitary, unimodal perceptual experience. So, light energy leads to the sensation of seeing, whereas sound waves produce the experience of hearing. However, for individuals with the rare phenomenon of synaesthesia, specific physical stimuli consistently induce more than one perceptual experience. For example, hearing particular sounds might induce vivid experiences of colour, taste or odour, as might the sight of visual symbols, such as letters or digits. Here we review the latest findings on synaesthesia, and consider its possible genetic, neural and cognitive bases. We also propose a neurocognitive framework for understanding such anomalous perceptual experiences.