Illusions are among our daily perceptions, but a more general answer to the question is the one given in the first chapter: Both illusions and veridical percepts must be manifestations of the same lawful processes of perceptual functioning. Therefore, we stand to gain as much knowledge by studying the one as by studying the other, and ultimately our theories must be able to explain both. Research on geometrical illusions has been active for over a century, but—–and this is an embarrassment to investigators in perception—–they remain, for the most part, unexplained. Of course, progress has been made and theories have been advanced, but, as we shall see, no one theory does justice to them all. Rather than attempt to catalogue all the known illusions, I will restrict the discussion to just a few of them. They are among the better known and can serve the purpose of illustrating the major theories.