Although COVID-19 is predominantly a respiratory disease, it is known to affect multiple organ systems. In this article, we highlight the impact of SARS-CoV-2 (the coronavirus causing COVID-19) on the central nervous system as there is an urgent need to understand the longitudinal impacts of COVID-19 on brain function, behaviour and cognition. Furthermore, we address the possibility of intergenerational impacts of COVID-19 on the brain, potentially via both maternal and paternal routes. Evidence from preclinical models of earlier coronaviruses has shown direct viral infiltration across the blood–brain barrier and indirect secondary effects due to other organ pathology and inflammation. In the most severely ill patients with pneumonia requiring intensive care, there appears to be additional severe inflammatory response and associated thrombophilia with widespread organ damage, including the brain. Maternal viral (and other) infections during pregnancy can affect the offspring, with greater incidence of neurodevelopmental disorders, such as autism, schizophrenia and epilepsy. Available reports suggest possible vertical transmission of SARS-CoV-2, although longitudinal cohort studies of such offspring are needed. The impact of paternal infection on the offspring and intergenerational effects should also be considered. Research targeted at mechanistic insights into all aspects of pathogenesis, including neurological, neuropsychiatric and haematological systems alongside pulmonary pathology, will be critical in informing future therapeutic approaches. With these future challenges in mind, we highlight the importance of national and international collaborative efforts to gather the required clinical and preclinical data to effectively address the possible long-term sequelae of this global pandemic, particularly with respect to the brain and mental health.