RNA viruses exploit all known mechanisms of genetic variation to ensure their survival. Distinctive features of RNA virus replication include high mutation rates, high yields, and short replication times. As a consequence, RNA viruses replicate as complex and dynamic mutant swarms, called viral quasispecies. Mutation rates at defined genomic sites are affected by the nucleotide sequence context on the template molecule as well as by environmental factors. In vitro hypermutation reactions offer a means to explore the functional sequence space of nucleic acids and proteins. The evolution of a viral quasispecies is extremely dependent on the population size of the virus that is involved in the infections. Repeated bottleneck events lead to average fitness losses, with viruses that harbor unusual, deleterious mutations. In contrast, large population passages result in rapid fitness gains, much larger than those so far scored for cellular organisms. Fitness gains in one environment often lead to fitness losses in an alternative environment. An important challenge in RNA virus evolution research is the assignment of phenotypic traits to specific mutations. Different constellations of mutations may be associated with a similar biological behavior. In addition, recent evidence suggests the existence of critical thresholds for the expression of phenotypic traits. Epidemiological as well as functional and structural studies suggest that RNA viruses can tolerate restricted types and numbers of mutations during any specific time point during their evolution. Viruses occupy only a tiny portion of their potential sequence space. Such limited tolerance to mutations may open new avenues for combating viral infections.