Phylogenetic comparative methods are one of the most important parts of the morphometric toolkit for studies of morphological evolution. The assessment of repeated independent events of evolution of phenotypic and associated ecological-functional traits is still a starting point for the study of adaptation, but modern comparative approaches go beyond correlative methods, allowing for the modeling of evolutionary scenarios and analyses of trait evolution patterns. The evidence for adaptive change due to ecological diversification is stronger (even if still circumstantial) if models that predict increases in diversification rate fit the data well and the morphological changes are associated with ecological and functional changes. A large body of literature is dedicated to methodological and theoretical aspects of comparative methods, but in the context of univariate traits. On the other hand, biological shape is a complex trait, and morphometric data is essentially multivariate. Whereas most comparative methods allow for direct multivariate extensions, dimension reduction is an almost certain requirement due to the high dimensionality of morphometric data sets and the large number of evolutionary parameters that need to be estimated by comparative methods. Objective methods with considerable statistical support to determine data dimensionality exist, but the applied literature usually relies on subjective criteria to how many shape dimensions should be retained. The most appropriate calculation and interpretations of principal components, the most popular dimension reduction method, are also topics that should be considered more carefully in applications. The maturity of comparative methods and the development of model-based approaches linking macroevolutionary patterns and microevolutionary processes provide an exciting perspective for the study of morphological evolution.