Summary: The COVID-19 pandemic, caused by a coronavirus called SARS-CoV-2, is far from being controlled despite the great efforts that have been made throughout the world. In the past few months, the identification of new variants of concern (VOC): Alpha, Beta, Gamma and Delta, has highlighted the importance of tracking the emergence of mutations in the SARS-CoV-2 genome that impact transmissibility, virulence, and immune and neutralizing antibody escape. Understanding which variants are interesting or concerning, and why, requires a full appreciation of virus evolution and the genomic epidemiology of SARS-CoV-2.