SARS-CoV-2 causes persistent infections in a subset of individuals, which is a major clinical and public health problem that should be prioritised for further investigation for several reasons. First, persistent SARS-CoV-2 infection often goes unrecognised, and therefore might affect a substantial number of people, particularly immunocompromised individuals. Second, the formation of tissue reservoirs (including in non-respiratory tissues) might underlie the pathophysiology of the persistent SARS-CoV-2 infection and require new strategies for diagnosis and treatment. Finally, persistent SARS-CoV-2 replication, particularly in the setting of suboptimal immune responses, is a possible source of new, divergent virus variants that escape pre-existing immunity on the individual and population levels. Defining optimal diagnostic and treatment strategies for patients with persistent virus replication and monitoring viral evolution are therefore urgent medical and public health priorities.