Our review aims to highlight the neurological complications of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and the available treatments according to the existing literature, discussing the underlying mechanisms. Since the end of 2019, SARS-CoV-2 has induced a worldwide pandemic that has threatened numerous lives. Fever, dry cough, and respiratory symptoms are typical manifestations of COVID-19. Recently, several neurological complications of the central and peripheral nervous systems following SARS-CoV-2 infection have gained clinicians' attention. Encephalopathy, stroke, encephalitis/meningitis, Guillain–Barré syndrome, and multiple sclerosis are considered probable neurological signs of COVID-19. The virus may invade the nervous system directly or induce a massive immune inflammatory response via a “cytokine storm.” Specific antiviral drugs are still under study. To date, immunomodulatory therapies and supportive treatment are the predominant strategies. In order to improve the management of COVID-19 patients, it is crucial to monitor the onset of new neurological complications and to explore drugs/vaccines targeted against SARS-CoV-2 infection.