If each of the four nucleotides were represented equally in the genomes of viruses and the hosts they infect, each base would occur at a frequency of 25%. However, this is not observed in nature. Similarly, the order of nucleotides is not random (for example, in the human genome, guanine follows cytosine at a frequency of ~0.0125, or a quarter the number of times predicted by random representation). Codon usage and codon order are also non-random. Furthermore, nucleotide and codon biases vary between species. Such biases have various drivers, including cellular proteins that recognise specific patterns in nucleic acids, that once triggered, induce mutations or invoke intrinsic or innate immune responses. In this review we examine the types of compositional biases identified in viral genomes and current understanding of the evolutionary mechanisms underpinning these trends. Finally, we consider the potential for large scale synonymous recoding strategies to engineer RNA virus vaccines, including those with pandemic potential, such as influenza A virus and Severe Acute Respiratory Syndrome Coronavirus Virus 2.