In addition to the conventional respiratory symptoms, patients with COVID-19 can exhibit neurological complications. In this concise review, we aim to report the most frequent neurologic manifestations related to Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV2) infection. SARS-CoV2 can reach the central nervous system from the bloodstream or olfactory pathway by binding ACE-2 receptor and the spike protein protease TMPRSS2. Headache is reported in more than 10% of affected patients and loss of smell and taste disturbance are reported in a slightly smaller percentage of cases. Acute cerebrovascular events are diagnosed in less than 3% of COVID-19 patients, but those with more severe manifestations have cerebrovascular events in more than 6% of the cases, as reported by two retrospective studies from Italy and China. Moreover, five cases of large-vessel stroke have been described in low-symptomatic COVID-19 patients aging less than 50 years suggesting that SARS-CoV2 can be associated with an increase of the risk of stroke in relatively young people. Peripheral nerve diseases can be observed after an apparently uneventful SARS-CoV2. Based on a literature review, nine patients experienced Guillain-Barrè syndrome (GBS) and 6 of these needed mechanical ventilation. Two more cases have been described with Miller-Fisher syndrome or polyneuritis cranialis, both had rapidly resolving symptoms. In conclusion, nervous system symptoms can be observed during SARS-CoV2 infection of which headache and smell and taste disturbance are the main symptoms reported. Cerebrovascular complications can complicate the course of COVID-19 in apparently low-risk patients. GBS is a life-threatening manifestation of COVID-19.