Several large-scale electronic health records studies have reported increased diagnostic rates for neuropsychiatric disorders following Coronavirus disease 2019 [COVID-19 or severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2 infection)], but many questions remain. To highlight the issues, we selectively review this literature, focusing on mood disorder, anxiety disorder, psychotic disorder, and cognitive impairment ('brain fog'). Eight key questions are addressed, comprising: (i) the nature and magnitude of the risks; (ii) their association with severity of infection; (iii) their duration; (iv) whether the risks differ between adults and children, or between men and women; (v) whether prior vaccination protects against them; (vi) the risk profile associated with different SARS-CoV-2 strains; (vii) what the underlying mechanisms might be; and (viii) whether the sequelae can be predicted. We consider the major unknowns, the limitations of electronic health records for research in this area, and the use of additional approaches to help characterize and understand the neuropsychiatric burden of COVID-19.