Statistical phylogenetics is computationally intensive, resulting in considerable attention meted on techniques for parallelization. Codon-based models allow for independent rates of synonymous and replacement substitutions and have the potential to more adequately model the process of protein-coding sequence evolution with a resulting increase in phylogenetic accuracy. Unfortunately, due to the high number of codon states, computational burden has largely thwarted phylogenetic reconstruction under codon models, particularly at the genomic-scale. Here, we describe novel algorithms and methods for evaluating phylogenies under arbitrary molecular evolutionary models on graphics processing units (GPUs), making use of the large number of processing cores to efficiently parallelize calculations even for large state-size models.