The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) emerged in Wuhan, China and rapidly spread worldwide, with a vast majority of confirmed cases presenting with respiratory symptoms. Potential neurological manifestations and their pathophysiological mechanisms have not been thoroughly established. In this narrative review, we sought to present the neurological manifestations associated with coronavirus disease 2019 (COVID-19). Case reports, case series, editorials, reviews, case-control and cohort studies were evaluated, and relevant information was abstracted. Various reports of neurological manifestations of previous coronavirus epidemics provide a roadmap regarding potential neurological complications of COVID-19, due to many shared characteristics between these viruses and SARS-CoV-2. Studies from the current pandemic are accumulating and report COVID-19 patients presenting with dizziness, headache, myalgias, hypogeusia and hyposmia, but also with more serious manifestations including polyneuropathy, myositis, cerebrovascular diseases, encephalitis and encephalopathy. However, discrimination between causal relationship and incidental comorbidity is often difficult. Severe COVID-19 shares common risk factors with cerebrovascular diseases, and it is currently unclear whether the infection per se represents an independent stroke risk factor. Regardless of any direct or indirect neurological manifestations, the COVID-19 pandemic has a huge impact on the management of neurological patients, whether infected or not. In particular, the majority of stroke services worldwide have been negatively influenced in terms of care delivery and fear to access healthcare services. The effect on healthcare quality in the field of other neurological diseases is additionally evaluated.