Sterilizing immunity after vaccination is desirable to prevent the spread of infection from vaccinees, which can be especially dangerous in hospital settings while managing frail patients. Sterilizing immunity requires neutralizing antibodies at the site of infection, which for respiratory viruses such as SARS-CoV-2 implies the occurrence of neutralizing IgA in mucosal secretions. Systemic vaccination by intramuscular delivery induces no or low-titer neutralizing IgA against vaccine antigens. Mucosal priming or boosting, is needed to provide sterilizing immunity. On the other side of the coin, sterilizing immunity, by zeroing interhuman transmission, could confine SARS-CoV-2 in animal reservoirs, preventing spontaneous attenuation of virulence in humans as presumably happened with the endemic coronaviruses. We review here the pros and cons of each vaccination strategy, the current mucosal SARS-CoV-2 vaccines under development, and their implications for public health.