Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative pathogen of the recent pandemic of coronavirus disease 19 (COVID-19). As the infection spreads, there is increasing evidence of neurological and psychiatric involvement in COVID-19. Headache, impaired consciousness, and olfactory and gustatory dysfunctions are common neurological manifestations described in the literature. Studies demonstrating more specific and more severe neurological involvement such as cerebrovascular insults, encephalitis and Guillain-Barre syndrome are also emerging. Respiratory failure, a significant condition that leads to mortality in COVID-19, is hypothesized to be partly due to brainstem impairment. Notably, some of these neurological complications seem to persist long after infection. This review aims to provide an update on what is currently known about neurological involvement in patients with COVID-19 due to SARS-CoV-2 infection. In this review, we demonstrate invasion routes of SARS-CoV-2, provide evidence to support the neurotropism hypothesis of the virus, and investigate the pathological mechanisms that underlie neurological complications associated with SARS-CoV-2.