Most phylogenetic methods are model-based and depend on Markov models designed to approximate the evolutionary rates between nucleotides or amino acids. When Markov models are selected for analysis of alignments of these characters, it is assumed that they are close approximations of the evolutionary processes that gave rise to the data. A variety of methods have been developed for estimating the fit of Markov models, and some of these methods are now frequently used for the selection of Markov models. In a growing number of cases, however, it appears that the investigators have used the model-selection methods without acknowledging their inherent shortcomings. This chapter reviews the issue of model selection and model evaluation.