Much recent progress in evolutionary biology is based on the inference of ancestral states and past transformations in important traits on phylogenetic trees. These exercises often assume that the tree is known without error and that ancestral states and character change can be mapped onto it exactly. In reality, there is often considerable uncertainty about both the tree and the character mapping. Recently introduced Bayesian statistical methods enable the study of character evolution while simultaneously accounting for both phylogenetic and mapping uncertainty, adding much needed credibility to the reconstruction of evolutionary history.