New SARS-CoV-2 variants that have accumulated multiple mutations in the spike (S) glycoprotein enable increased transmission and resistance to neutralizing antibodies. Here, we study the antigenic and structural impacts of the S protein mutations from four variants, one that was involved in transmission between minks and humans, and three that rapidly spread in human populations and originated in the United Kingdom, Brazil or South Africa. All variants either retained or improved binding to the ACE2 receptor. The B.1.1.7 (UK) and B.1.1.28 (Brazil) spike variants showed reduced binding to neutralizing NTD and RBD antibodies, respectively, while the B.1.351 (SA) variant showed reduced binding to both NTD- and RBD-directed antibodies. Cryo-EM structural analyses revealed allosteric effects of the mutations on spike conformations and revealed mechanistic differences that either drive inter-species transmission or promotes viral escape from dominant neutralizing epitopes.