Two features of viral quasispecies are reviewed: the presence of memory genomes as minority components of their mutant spectra, and viral extinction due to enhanced mutagenesis. Memory has been documented with several genetic markers of the important animal picornavirus foot-and-mouth disease virus (FMDV). The presence of memory genomes in viral quasispecies may accelerate their adaptive response whenever a selective constraint has already been experienced by a viral population during previous stages of its evolution. Enhanced mutagenesis has been shown to lead to losses of infectivity of a number of RNA viruses: poliovirus, vesicular stomatitis virus, human immunodeficiency virus type 1 and FMDV. These observations, based on the theoretical prediction of the existence of a copying error-threshold for maintenance of genetic information, may contribute to the development of a new antiviral strategy.