The genetic code is degenerate--most amino acids can be encoded by from two to as many as six different codons. The synonymous codons are not used with equal frequency: not only are some codons favored over others, but also their usage can vary significantly from species to species and between different genes in the same organism. Known causes of codon bias include differences in mutation rates as well as selection pressure related to the expression level of a gene, but the standard analysis methods can account for only a fraction of the observed codon usage variation. We here introduce an explicit model of codon usage bias, inspired by statistical physics. Combining this model with a maximum likelihood approach, we are able to clearly identify different sources of bias in various genomes. We have applied the algorithm to Saccharomyces cerevisiae as well as 325 prokaryote genomes, and in most cases our model explains essentially all observed variance.