Viral quasispecies are closely related (but nonidentical) mutant and recombinant viral genomes subjected to continuous genetic variation, competition, and selection. Quasispecies structure and dynamics of replicating RNA enable virus populations to persist in their hosts and cause disease. We review mechanisms of viral persistence in cells, organisms, and populations of organisms and suggest that the critical interplay between host and viral influences (including in some cases the quasispecies organization) is the main driving force for long-term survival of viruses in nature.