RNA viruses get extinct in a process called lethal mutagenesis when subjected to an increase in their mutation rate, for instance, by the action of mutagenic drugs. Several approaches have been proposed to understand this phenomenon. The extinction of RNA viruses by increased mutational pressure was inspired by the concept of the error threshold. The now classic quasispecies model predicts the existence of a limit to the mutation rate beyond which the genetic information of the wild type could not be efficiently transmitted to the next generation. This limit was called the error threshold, and for mutation rates larger than this threshold, the quasispecies was said to enter into error catastrophe. This transition has been assumed to foster the extinction of the whole population. Alternative explanations of lethal mutagenesis have been proposed recently. In the first place, a distinction is made between the error threshold and the extinction threshold, the mutation rate beyond which a population gets extinct. Extinction is explained from the effect the mutation rate has, throughout the mutational load, on the reproductive ability of the whole population. Secondly, lethal defection takes also into account the effect of interactions within mutant spectra, which have been shown to be determinant for the understanding the extinction of RNA virus due to an augmented mutational pressure. Nonetheless, some relevant issues concerning lethal mutagenesis are not completely understood yet, as so survival of the flattest, i.e. the development of resistance to lethal mutagenesis by evolving towards mutationally more robust regions of sequence space, or sublethal mutagenesis, i.e., the increase of the mutation rate below the extinction threshold which may boost the adaptability of RNA virus, increasing their ability to develop resistance to drugs (including mutagens). A better design of antiviral therapies will still require an improvement of our knowledge about lethal mutagenesis.