The consensus among evolutionists seems to be that the morphological complexity of organisms increases in evolution, although almost no empirical evidence for such a trend exists. Most studies of complexity have been theoretical, and the few empirical studies have not, with the exception of certain recent ones, been especially rigorous; reviews are presented of both the theoretical and empirical literature. The paucity of evidence raises the question of what sustains the consensus, and a number of suggestions are offered, including the (...) possibility that certain cultural and/or perceptual biases are at work. In addition, a shift in emphasis from theoretical to empirical inquiry is recommended for the study of complexity, and guidelines for future empirical studies are proposed. (shrink)