This book introduces Markovian codon models of evolution in maximum likelihood phylogeny inference. The literature show that codon models constitute a more realistic representation of protein-coding sequences when compared against amino acid and nucleotide models. Our results extend this by showing that codon models are also expected to outperform these two competing approaches when re-constructing phylogenetic trees. To enable this analysis, we have created a software package called CodonPhyml, which is freely available under an open source license.