Viruses are fast evolving pathogens that continuously adapt to the highly variable environments they live and reproduce in. Strategies devoted to inhibit virus replication and to control their spread among hosts need to cope with these extremely heterogeneous populations and with their potential to avoid medical interventions. Computational techniques such as phylogenetic methods have broadened our picture of viral evolution both in time and space, and mathematical modeling has contributed

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... antially to our progress in unraveling the dynamics of virus replication, fitness, and virulence. Integration of multiple computational and mathematical approaches with experimental data can help to predict the behavior of viral pathogens and to anticipate their escape dynamics. This piece of information plays a critical role in some aspects of vaccine development, such as viral strain selection for vaccinations or rational attenuation of viruses. Here we review several aspects of viral evolution that can be addressed quantitatively, and we discuss computational methods that have the potential to improve vaccine design.