In this review, we address issues that relate to the rapid “Warp Speed” development of vaccines to counter the COVID-19 pandemic. We review the antibody response that is triggered by SARS-CoV-2 infection of humans, and how it may inform vaccine research. The isolation and properties of neutralizing monoclonal antibodies from COVID-19 patients provide additional information on what vaccines should try to elicit. The nature and longevity of the antibody response to coronaviruses are relevant to the potency and duration of vaccine-induced immunity. We summarize the immunogenicity of leading vaccine candidates tested to date in animals and humans, and discuss the outcome and interpretation of virus-challenge experiments. By far the most immunogenic vaccine candidates for antibody responses are recombinant proteins, which are not represented in the “Warp Speed” program. A substantial concern for SARS-CoV-2 vaccines is adverse events, which we review by considering what was seen in studies of SARS-CoV-1 and MERS-CoV vaccines. We conclude by outlining the possible outcomes of the “Warp Speed” vaccine program.