Despite its importance to evolutionary theory, convergence remains an understudied phenomenon and is usually investigated using qualitative data. This paper advances a new, multidimensional view of convergence. Three patterns indicative of convergence are discussed, and techniques to discover and test convergent patterns in a quantitative framework are developed. These concepts and methods are applied to a dataset of digitized coordinates on 1554 lizard skulls and 1292 lower jaws to test hypotheses of convergence among herbivorous lizards. Encompassing seven independent acquisitions of herbivory, this lizard sample provides an ideal natural experiment for exploring ideas of convergence among different systems (here, morphological and functional). Three related questions are addressed: (1) Do herbivorous lizards show evidence of convergence in skull and lower jaw morphology? (2) What, if any, is the morphospace pattern associated with this convergence? (3) Is it possible to predict the direction of convergence using functional models? Relative warp analysis and permutation tests reveal that the skulls and lower jaws of herbivorous lizards do show evidence of convergence. Herbivore skulls deviate from their carnivorous or omnivorous sister groups toward the same area of morphospace. Without a phylogenetic perspective, this pattern would not be recognizable. Lower jaws of herbivores are not convergent in morphology but are convergent in function: herbivores deviate away from their carnivorous sister groups toward higher values of mechanical advantage. These results illustrate the desirability of quantitative methods, informed by phylogenetic information, in the study of convergence.