The pattern and strength of genetic covariation is shaped by selection so that it is strong among functionally related characters and weak among functionally unrelated characters. Genetic covariation is expressed as phenotypic covariation within species and acts as a constraint on evolution by limiting the ability of linked characters to evolve independently of one another. Such linked characters are "constrained" and are expected to express covariation both within and among species. In this study, the pattern and magnitude of covariation among aspects of dental size and shape are investigated in anthropoid primates. Pleiotropy has been hypothesized to play a significant role in derivation of derived hominin morphologies. This study tests a series of hypotheses; including 1) that negative within- and among-species covariation exists between the anterior (incisors and canines) and postcanine teeth, 2) that covariation is strong and positive between the canines and incisors, 3) that there is a dimorphic pattern of within-species covariation and coevolution for characters of the canine honing complex, 4) that patterns of covariation are stable among anthropoids, and 5) that genetic constraints have been a strong bias on the diversification of anthropoid dental morphology. The study finds that patterns of variance-covariance are conserved among species. Despite these shared patterns of variance-covariance, dental diversification has frequently occurred along dimensions not aligned with the vector of genetic constraint. As regards the canine honing complex, there is no evidence for a difference in the pleiotropic organization or the coevolution of characters of the complex in males and females, which undermines arguments that the complex is selectively important only in males. Finally, there is no evidence for strong or negative pleiotropy between any dental characters, which falsifies hypotheses that predict such relationships between incisors and postcanine teeth or between the canines and the postcanine teeth.