For centuries, philosophers and psychologists have distinguished between correct or veridical perception and illusory perception. Illusions have become an essential topic in textbooks on perception, and we amuse our lecture classes with demonstrations that reveal the fallibility of perceptual systems--what we see, hear, feel, taste, and smell does not correspond to what is really there. This special issue of Perception contains the descriptions of many new and interesting illusions as well as speculations about the causes of familiar illusions. There have also been many attempts to classify illusions that date back to Al-Haytham (1083) in the 11th century through to Richard Gregory (2009 Seeing through Illusions, Oxford: Oxford University Press) in the last decade, but there have been far fewer attempts to analyse and critique the concept itself. That is the purpose of this paper, and the conclusion reached is that there is no satisfactory way of distinguishing between those aspects of our perception that we regard as veridical and those we label as illusions.