In humans, several respiratory viruses can have neurologic implications affecting both central and peripheral nervous system. Neurologic manifestations can be linked to viral neurotropism and/or indirect effects of the infection due to endothelitis with vascular damage and ischemia, hypercoagulation state with thrombosis and hemorrhages, systemic inflammatory response, autoimmune reactions, and other damages. Among these respiratory viruses, recent and huge attention has been given to the coronaviruses, especially the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic started in 2020. Besides the common respiratory symptoms and the lung tropism of SARS-CoV-2 (COVID-19), neurologic manifestations are not rare and often present in the severe forms of the infection. The most common acute and subacute symptoms and signs include headache, fatigue, myalgia, anosmia, ageusia, sleep disturbances, whereas clinical syndromes include mainly encephalopathy, ischemic stroke, seizures, and autoimmune peripheral neuropathies. Although the pathogenetic mechanisms of COVID-19 in the various acute neurologic manifestations are partially understood, little is known about long-term consequences of the infection. These consequences concern both the so-called long-COVID (characterized by the persistence of neurological manifestations after the resolution of the acute viral phase), and the onset of new neurological symptoms that may be linked to the previous infection.