Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causative agent of coronavirus disease 2019, contributes to neurological pathologies in nearly 30% of patients, extending beyond respiratory symptoms. These manifestations encompass disorders of both the peripheral and central nervous systems, causing among others cerebrovascular issues and psychiatric manifestations during the acute and/or post-acute infection phases. Despite ongoing research, uncertainties persist about the precise mechanism the virus uses to infiltrate the central nervous system and the involved entry portals. This review discusses the potential entry routes, including hematogenous and anterograde transport. Furthermore, we explore variations in neurotropism, neurovirulence, and neurological manifestations among pandemic-associated variants of concern. In conclusion, SARS-CoV-2 can infect numerous cells within the peripheral and central nervous system, provoke inflammatory responses, and induce neuropathological changes.