Character mapping on phylogenies has played an important, if not critical role, in our understanding of molecular, morphological, and behavioral evolution. Until very recently we have relied on parsimony to infer character changes. Parsimony has a number of serious limitations that are drawbacks to our understanding. Recent statistical methods have been developed that free us from these limitations enabling us to overcome the problems of parsimony by accommodating uncertainty in evolutionary time, ancestral states, and the phylogeny.