The field of molecular evolution, which includes genome evolution, is devoted to finding variation within and between groups of organisms and explaining the processes responsible for generating this variation. Many DNA changes are believed to have little to no functional effect, and a neutral process will best explain their evolution. Thus, a central task is to discover which changes had positive fitness consequences and were subject to Darwinian natural selection during the course of evolution. Due the size and complexity of modern molecular datasets, the field has come to rely extensively on statistical modeling techniques to meet this analytical challenge. For DNA sequences that encode proteins, one of the most powerful approaches is to employ a statistical model of codon evolution. This unit provides a general introduction to the practice of modeling codon evolution using the statistical framework of maximum likelihood. Four real-data analysis activities are used to illustrate the principles of parameter estimation, robustness, hypothesis testing, and site classification. Each activity includes an explicit analytical protocol based on programs provided by the Phylogenetic Analysis by Maximum Likelihood (PAML) package.