A generalization of the concept of a spinor that involves the use of complex numbers in an essential way. Twistors were invented by Roger Penrose in the hope that they would be a key concept in unifying the general theory of relativity and quantum mechanics. They have not done so yet, although some very intriguing relations have been established between twistors and noncommutative geometry, supergravity theory, superstring theory, and supersymmetry. Twistors have also proved useful for finding soliton solutions to gauge theories.