Aphthoviruses are an important group of animal pathogens. A combination of genetic and structural studies has revealed one of the main principles governing their evolution: severe limitations to variation imposed by functional and structural constraints, in conjunction with high mutation and recombination rates operating during genome replication. Evolution occurs by positive selection and random drift acting on complex quasispecies distributions. The mutant composition of a quasi-species (or mutant spectrum) is largely dictated by tolerance to nucleotide and amino acid substitutions in viral RNAs and proteins, which must remain functionally competent. We review recent evidence to support this proposal, and we suggest that similar concepts may apply to other RNA viruses as well.