Over the course of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic, the clinical, scientific, and public health communities have had to respond to new viral genetic variants. Each one has triggered a flurry of media attention, a range of reactions from the scientific community, and calls from governments to either “stay calm” or pursue immediate countermeasures. While many scientists were initially sceptical about the significance of the D614G alteration, the emergence of the new “UK variant”—lineage B.1.1.7—has raised widespread concern. Understanding which variants are concerning, and why, requires an appreciation of viral evolution and the genomic epidemiology of SARS-CoV-2. In this perspective, the authors discussed these issues focusing on the different mutations, variants, potential spread, antigenicity and vaccine effectiveness.