SARS-CoV-2 virus was first identified in 2019 in Wuhan (China) and is responsible for the ongoing COVID-19 pandemic. Although the virus causes mild, transient symptoms of an upper respiratory tract infection in most cases, it can also lead to severe pneumonia, respiratory failure and/or death. Approximately 85% of patients experience central and peripheral neurological symptoms. In the acute phase of the disease, ischaemic strokes, intracranial haemorrhages, meningitis and encephalitis, acute demyelinating diseases and acute inflammatory polyneuropathies may occur. However, mild neurological symptoms that can persist for months and significantly affect daily functioning are much more common. These include headache and dizziness, olfactory and gustatory dysfunction, mild cognitive disturbances, as well as depressive, anxiety, and sleep disorders. Some of them are encompassed by popular terms “post-covid syndrome” and “brain fog.” The pathogenesis of neurological complications of SARS-CoV-2 infection is still not fully understood; overproduction of cytokines induced by viral infection may be of great importance. There is no causal treatment, while symptomatic treatment is of limited effectiveness. Primary prevention in the form of SARS-CoV-2 vaccinations is of great importance. In the following review, we would like to present the current knowledge on epidemiology, pathology, pathogenesis and treatment of neurological complications after SARS-CoV-2 infection. Further multi-centre, large-scale clinical studies are necessary to identify the exact pathogenetic mechanisms.