Coronavirus disease 2019 (COVID-19), an infection caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is currently hitting the world in the form of a pandemic. Given that some reports suggest that this infection can also occur with neurologic manifestations, this narrative review addresses the basic and clinical aspects concerning the nervous system involvement associated with this disease. More than one third of patients hospitalized for COVID-19 can present with both central and peripheral neurological manifestations. The former include dizziness and headache, while the latter include taste and smell disturbances. Other reported neurological manifestations are cerebrovascular disease and epileptic seizures. According to published reports, neurological disorders are not uncommon in COVID-19 and can sometimes represent the first manifestation of the disease; therefore, neurologists should consider this diagnostic possibility in their daily practice. Since maybe not all COVID-19 neurological manifestations are due to SARS-CoV-2 direct effects, it is important to monitor the rest of the clinical parameters such as, for example, oxygen saturation. Similarly, follow-up of patients is advisable, since whether neurological complications may develop lately is thus far unknown.