Despite advances in the treatment and mitigation of critical illness caused by infection with SARS-CoV-2, millions of survivors have a devastating, post-acute infection syndrome known as long COVID. A large proportion of patients with long COVID have nervous system dysfunction, which is also seen in the distinct but overlapping condition of post-intensive care syndrome (PICS), putting survivors of COVID-19-related critical illness at high risk of long-lasting morbidity affecting multiple organ systems and, as a result, engendering measurable deficits in quality of life and productivity. In this Series paper, we discuss neurological, cognitive, and psychiatric sequelae in patients who have survived critical illness due to COVID-19. We review current knowledge of the epidemiology and pathophysiology of persistent neuropsychological impairments, and outline potential preventive strategies based on safe, evidence-based approaches to the management of pain, agitation, delirium, anticoagulation, and ventilator weaning during critical illness. We highlight priorities for current and future research, including possible therapeutic approaches, and offer considerations for health services to address the escalating health burden of long COVID.