Developments in the study of superluminal motions in quasars are reviewed. Theorists explain the apparent motion as an illusion due to radio sources moving with a relativistic but subluminal velocity at an angle small with respect to the observer's line of sight. Independent evidence for the existence of such motion is summarized. Statistical studies of 'classical double' radio quasars, aimed at finding evidence for the small angles to the observer's line of sight, have found an uncomfortably large number of superluminal compact cores. Faint outer double structures have been found in all but one of the sources, and the outer structures are apparently not at the required small angle to the line of sight. Browne's scheme to explain this effect by interpreting all radio quasars as members of a single class is discussed, as is a model in which the line of sight angle problem is resolved by having the plasma emerge in a spray of directions which are later recollimated.