Most COVID-19 vaccines are designed to elicit immune responses, ideally neutralizing antibodies (NAbs), against the SARS-CoV-2 spike protein. Several vaccines, including mRNA, adenoviral-vectored, protein subunit and whole-cell inactivated virus vaccines, have now reported efficacy in phase III trials and have received emergency approval in many countries. The two mRNA vaccines approved to date show efficacy even after only one dose, when non-NAbs and moderate T helper 1 cell responses are detectable, but almost no NAbs. After a single dose, the adenovirus vaccines elicit polyfunctional antibodies that are capable of mediating virus neutralization and of driving other antibody-dependent effector functions, as well as potent T cell responses. These data suggest that protection may require low levels of NAbs and might involve other immune effector mechanisms including non-NAbs, T cells and innate immune mechanisms. Identifying the mechanisms of protection as well as correlates of protection is crucially important to inform further vaccine development and guide the use of licensed COVID-19 vaccines worldwide.