Evolution has several narratives and formulations, and their integration is a pending challenge. RNA viruses, the most abundant subcellular replicative entities in the biosphere, are part of a widespread class of RNA genetic elements that evolve at rates that exceed by almost a million-fold the rates exhibited by their host organisms. Since they use the same tools for genome variation as cells, viruses have been highly informative of molecular and population dynamics routes for adaptation and persistence. Here, we review basic features of viral RNA evolution, including new observations obtained by application of ultra-deep sequencing to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) populations. Mutual interactions between complex arrays of variant genomes and host cells underlie a number of implications for viral pathogenesis and the control of viral disease. Genome variations, which are largely presided by stochastic events, can give rise to emergent phenotypic traits in what has been termed “quasispecies productivity.” It relates to tinkering in evolutionary constructions, as expressed by F. Jacob 50 years ago. By virtue of their accelerated evolution, RNA viruses can help in the understanding of biological complexity as an input for evolutionary processes.