Several fast-spreading variants of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have become the dominant circulating strains in the COVID-19 pandemic. We report here cryo–electron microscopy structures of the full-length spike (S) trimers of the B.1.1.7 and B.1.351 variants, as well as their biochemical and antigenic properties. Amino acid substitutions in the B.1.1.7 protein increase both the accessibility of its receptor binding domain and the binding affinity for receptor angiotensin-converting enzyme 2 (ACE2). The enhanced receptor engagement may account for the increased transmissibility. The B.1.351 variant has evolved to reshape antigenic surfaces of the major neutralizing sites on the S protein, making it resistant to some potent neutralizing antibodies. These findings provide structural details on how SARS-CoV-2 has evolved to enhance viral fitness and immune evasion.