The coronavirus disease COVID-19 began to spread worldwide in December 2019 from the city of Wuhan (China). COVID-19 is often accompanied by fever, hypoxemic respiratory failure and systemic complications (for example, gastrointestinal, renal, cardiac, neurological, and hepatic lesions), thrombotic phenomena. Central nervous system damage is caused by the primary effect on it, direct neuroinvasion of the virus, and more often by secondary effect due to systemic hyperinflammation. Neurological manifestations include fatigue, headache, insomnia, and olfactory/taste disorders. Neurological manifestations and complications of COVID-19 are diverse: (1) cerebral circulatory disorders, including ischemic stroke and macro/microhemorrhages; (2) encephalopathy; (3) para/postinfectious autoimmune complications, such as GuillainBarre syndrome; (4) meningoencephalitis; (5) neuropsychiatric complications (psychosis and mood disorders). In terms of pathogenesis, neurological disorders in COVID-19 can be caused by neurotropicity and neurovirulence of SARS-CoV-2, cytokine storm, hypoxemia, homeostasis disorders, as well as their combined effects. COVID-19 adversely affects the course and prognosis of chronic neurological disorders in comorbid patients. The review highlights the need for vigilance to early neurological complications in patients infected with SARS-CoV-2 and other coronaviruses, especially since some neurological complications may precede respiratory manifestations.