Evolutionary quantitative genetics provides a strong theoretical framework for connecting evolutionary processes, the underlying genetic architecture of traits, described in terms of variances and covariances, and the pace and direction of multivariate evolution. In this talk I will discuss the importance of considering a multidimensional phenotype and the within-species (co)variation to understand trait dynamics in populations, in terms of evolvability (i.e., the ability of a biological system to respond to selection) and evolutionary constraints. I will explore the evolution of the cranial covariance structure and the average morphology in the most noteworthy example of adaptive radiation in mammals, the New World leaf-nosed bats, by combining phylogenetic comparative methods and quantitative genetic approaches.