The pandemic of COVID-19, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is far from being controlled despite the great effort that have been taken throughout the world. Herd immunity through vaccination is our major expectation to rein the virus. However, the emergence of widespread genetic variants could potentially undermine the vaccines. The evidence that some variants could evade immune responses elicited by vaccines and previous infection is growing. In this review, we summarized the current understanding on five notable genetic variants, i.e., D614G, Cluster 5, VOC 202012/01, 501Y.V2 and P.1, and discussed the potential impact of these variants on the virus transmission, pathogenesis and vaccine efficacy. We also highlight that mutations in the N-terminal domain of spike protein should be considered when evaluating the antibody neutralization abilities. Among these genetic variants, a concern of genetic variant 501Y.V2 to escape the protection by vaccines was raised. We therefore call for new vaccines targeting this variant to be developed.