Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is more than merely a respiratory disease, as it also presents with various neurological symptoms. SARS-CoV-2 may infect the central nervous system (CNS) and thus is neurotropic. However, the pathophysiological mechanism of coronavirus disease 2019 (COVID-19)-associated neuropathy remains unclear. Many studies have reported that SARS-CoV-2 enters the CNS through the hematogenous and neuronal routes, as well as through the main host neurological immune responses and cells involved in these responses. The neurological immune responses to COVID-19 and potential mechanisms of the extensive neuroinflammation induced by SARS-CoV-2 have been investigated. Although CNS infection with SARS-CoV-2 was shown to lead to neuronal impairment, certain aspects of this mechanism remain controversial and require further analysis. In this review, we discussed the pathway and mechanisms of SARS-CoV-2 invasion in the CNS, and associated clinical manifestations, such as anosmia, headache, and hyposmia. Moreover, the mechanism of neurological damage caused by SARS-CoV-2 may provide potential treatment methods for patients presenting with SARS-CoV-2-associated neuropathy.