This article reviews theoretical and empirical arguments for and against various theories that explain the classic Ponzo illusion and its variants from two different viewpoints concerning the role of perceived depth in size distortions. The first viewpoint argues that all Ponzo-like illusions are driven by perceived depth. The second viewpoint argues that the classic Ponzo illusion is unrelated to depth perception. This review will give special focus to the first viewpoint and consists of three sections. In the first section, the role of the number of pictorial depth cues and previous experience in the strength of all Ponzo-like illusions are discussed. In the second section, we contrast the first viewpoint against the theories that explain the classic Ponzo illusion with mechanisms that are unrelated to depth perception. In the last section, we propose a Bayesian-motivated reconceptualization of Richard Gregory's misapplied size constancy theory that explains Ponzo-variant illusions in terms of prior information and prediction errors. The new account explains why some studies have provided inconsistent evidence for misapplied size constancy theory.