Studies of character evolution often assume that a phylogeny's shape is determined independently of the characters, which then evolve as mere passengers along the tree's branches. However, if the characters help shape the tree, but this is not considered, biased inferences can result. Simulations of asymmetrical speciation (i.e., one character state conferring a higher rate of speciation than another) result in data that are interpreted to show a higher rate of change toward the diversification-enhancing state, even though the rates to and from this state were in fact equal. Conversely, simulations of asymmetrical character change yield data that could be misinterpreted as showing asymmetrical rates of speciation. Studies of biased diversification and biased character change need to be unified by joint models and estimation methods, although how successfully the two processes can be teased apart remains to be seen.