Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), a novel coronavirus, is responsible for the outbreak of coronavirus disease 19 (COVID-19) and was first identified in Wuhan, China in December 2019. It is evident that the COVID-19 pandemic has become a challenging world issue. Although most COVID-19 patients primarily develop respiratory symptoms, an increasing number of neurological symptoms and manifestations associated with COVID-19 have been observed. In this narrative review, we elaborate on proposed neurotropic mechanisms and various neurological symptoms, manifestations, and complications of COVID-19 reported in the present literature. For this purpose, a review of all current published literature (studies, case reports, case series, reviews, editorials, and other articles) was conducted and neurological sequelae of COVID-19 were summarized. Essential and common neurological symptoms including gustatory and olfactory dysfunctions, myalgia, headache, altered mental status, confusion, delirium, and dizziness are presented separately in sections. Moreover, neurological manifestations and complications that are of great concern such as stroke, cerebral (sinus) venous thrombosis, seizures, meningoencephalitis, Guillain-Barré syndrome, Miller Fisher syndrome, acute myelitis, and posterior reversible encephalopathy syndrome (PRES) are also addressed systematically. Future studies that examine the impact of neurological symptoms and manifestations on the course of the disease are needed to further clarify and assess the link between neurological complications and the clinical outcome of patients with COVID-19. To limit long-term consequences, it is crucial that healthcare professionals can early detect possible neurological symptoms and are well versed in the increasingly common neurological manifestations and complications of COVID-19.