Infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has become pandemic and the duration of protective immunity to the virus is unknown. Cases of persons reinfected with the virus are being reported with increasing frequency. At present it is unclear how common reinfection with SARS-CoV-2 is and how long serum antibodies and virus-specific T cells persist after infection. For many other respiratory virus infections, including influenza and the seasonal coronaviruses that cause colds, serum antibodies persist for only months to a few years and reinfections are very common. Here we review what is known about the duration of immunity and reinfection with coronaviruses, including SARS-CoV-2, as well as the duration of immunity to other viruses and virus vaccines. These findings have implications for the need of continued protective measures and for vaccines for persons previously infected with SARS-CoV-2.