Background: The genetic variability of SARS-CoV-2 has increased notably since the pandemic was declared, which has allowed it to represent a continuous challenge for health policies aimed at its control. Objective. Describe the genomic nomenclature used for general and scientific communication about SARS-CoV-2, as well as describe the mutations, evolution, origin and variants of the virus. Material and Methods. A narrative literature review was carried out, for which a search and analysis of the information was carried out until December 15, 2021. 74 sources selected from the MEDLINE / PubMed, SciELO, LILACS databases and official web pages were reviewed; no language restrictions. Results. Mutations are changes in the nucleotide sequence of the viral genome, which, by affecting the epidemiological dynamics in a population, give rise to variants, and these in turn to differentiated clades. Among the variants of interest, Lambda and Mu stand out, identified for the first time in Peru and Colombia, respectively. While, the variants of concern, in chronological order, are Alpha (British), Beta (South African), Gamma (Brazilian), Delta (Indian) and recently Ómicron. Conclusions. It is concluded that the genomic diversity of SARS-CoV-2 is due to its high rate of mutations that can constitute variants and clades. A better understanding of this diversity allows more effective control measures to be taken, guiding the development and use of vaccines, therapies, diagnostics and health policies.