The human infection of the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a public health emergency of international concern that has caused more than 16.8 million new cases and 662,000 deaths as of July 30, 2020. Although coronavirus disease 2019 (COVID-19), which is associated with this virus, mainly affects the lungs, recent evidence from clinical and pathological studies indicates that this pathogen has a broad infective ability to spread to extrapulmonary tissues, causing multiorgan failure in severely ill patients. In this regard, there is increasing preoccupation with the neuroinvasive potential of SARS-CoV-2 due to the observation of neurological manifestations in COVID-19 patients. This concern is also supported by the neurotropism previously documented in other human coronaviruses, including the 2002-2003 SARS-CoV-1 outbreak. Hence, in the current review article, we aimed to summarize the spectrum of neurological findings associated with COVID-19, which include signs of peripheral neuropathy, myopathy, olfactory dysfunction, meningoencephalitis, Guillain-Barré syndrome, and neuropsychiatric disorders. Furthermore, we analyze the mechanisms underlying such neurological sequela and discuss possible therapeutics for patients with neurological findings associated with COVID-19. Finally, we describe the host-and pathogen-specific factors that determine the tissue tropism of SARS-CoV-2 and possible routes employed by the virus to invade the nervous system from a pathophysiological and molecular perspective. In this manner, the current manuscript contributes to increasing the current understanding of the neurological aspects of COVID-19 and the impact of the current pandemic on the neurology field.