The Covid-19 pandemic has ravaged the globe, and its causative agent, SARS-CoV-2, continues to rage. Prospects of ending this pandemic rest on the development of effective interventions. Two monoclonal antibody (mAb) therapeutics have received emergency use authorization, and more are in the pipeline. Furthermore, multiple vaccine constructs have shown promise, including two with ~95% protective efficacy against Covid-19. However, these interventions were directed toward the initial SARS-CoV-2 that emerged in 2019. Considerable viral evolution has occurred since, including variants with a D614G mutation that have become dominant. Viruses with this mutation alone do not appear to be antigenically distinct, however. Recent emergence of new SARS-CoV-2 variants B.1.1.7 in the UK and B.1.351 in South Africa is of concern because of their purported ease of transmission and extensive mutations in the spike protein. We now report that B.1.1.7 is refractory to neutralization by most mAbs to the N-terminal domain (NTD) of spike and relatively resistant to a number of mAbs to the receptor-binding domain (RBD). It is modestly more resistant to convalescent plasma (~3 fold) and vaccinee sera (~2 fold). Findings on B.1.351 are more worrisome in that this variant is not only refractory to neutralization by most NTD mAbs but also by multiple potent mAbs to the receptor-binding motif on RBD, largely due to an E484K mutation. Moreover, B.1.351 is markedly more resistant to neutralization by convalescent plasma (~11-33 fold) and vaccinee sera (~6.5-8.6 fold). B.1.351 and emergent variants with similar spike mutations present new challenges for mAb therapy and threaten the protective efficacy of current vaccines.