Rapidly emerging SARS-CoV-2 variants jeopardize antibody-based countermeasures. Although cell culture experiments have demonstrated a loss of potency of several anti-spike neutralizing antibodies against variant strains of SARS-CoV-21–3, the in vivo importance of these results remains uncertain. Here we report the in vitro and in vivo activity of a panel of monoclonal antibodies (mAbs), which correspond to many in advanced clinical development by Vir Biotechnology, AbbVie, AstraZeneca, Regeneron and Lilly, against SARS-CoV-2 variant viruses. Although some individual mAbs showed reduced or abrogated neutralizing activity in cell culture against B.1.351, B.1.1.28, B.1.617.1 and B.1.526 viruses with mutations at residue E484 of the spike protein, low prophylactic doses of mAb combinations protected against infection by many variants in K18-hACE2 transgenic mice, 129S2 immunocompetent mice and hamsters, without the emergence of resistance. Exceptions were LY-CoV555 monotherapy and LY-CoV555 and LY-CoV016 combination therapy, both of which lost all protective activity, and the combination of AbbVie 2B04 and 47D11, which showed a partial loss of activity. When administered after infection, higher doses of several mAb cocktails protected in vivo against viruses with a B.1.351 spike gene. Therefore, many—but not all—of the antibody products with Emergency Use Authorization should retain substantial efficacy against the prevailing variant strains of SARS-CoV-2.