Robustness describes the capacity for a biological system to remain canalized despite perturbation. Genetic robustness affords maintenance of phenotype despite mutational input, necessarily involving the role of epistasis. Environmental robustness is phenotypic constancy in the face of environmental variation, where epistasis may be uninvolved. Here we discuss genetic and environmental robustness, from the standpoint of infectious disease evolution, and suggest that robustness may be a unifying principle for understanding how different disease agents evolve. We focus especially on viruses with RNA genomes due to their importance in the evolution of emerging diseases and as model systems to test robustness theory. We present new data on adaptive constraints for a model RNA virus challenged to evolve in response to UV radiation. We also draw attention to other infectious disease systems where robustness theory may prove useful for bridging evolutionary biology and biomedicine, especially the evolution of antibiotic resistance in bacteria, immune evasion by influenza, and malaria parasite infections.