The recent simultaneous appearance of numerous highly contagious variants of SARS-CoV-2 demonstrate that the rate of adaptive evolution in the SARS-CoV-2 population is accelerating. It is no longer appropriate to focus only on epidemiological goals like flattening the curve and vaccinating to achieve herd immunity. We are now in a new phase of the pandemic, in which we must also focus on the evolutionary threats. Here, we use the tools of population genetics, a subfield of evolutionary biology, to look into the pandemic’s past and future. We explain why these variants are arising with increasing frequency as the size of the pandemic grows and we explore the likely paths of future SARS-CoV-2 evolution. Our take-home message is that viral evolution during the vaccine rollout will be especially serious, making it essential to bring case counts down immediately.