Viral infections have detrimental impacts on neurological functions, and even to cause severe neurological damage. Very recently, coronaviruses (CoV), particularly SARS-CoV-2 display neurotropic properties and may also cause neurological diseases. It is reported that CoV can be found in the brain or cerebrospinal fluid. The pathobiology of these neuroinvasive viruses is still incompletely known, and it is therefore important to explore the impact of CoV infections on the nervous system. Here, we review the research into neurological complications in SARS-CoV-2 infections and the possible mechanisms of damage to the nervous system. Given the taxonomic similarity between SARS-CoV and SARS-CoV-2, it is plausible that patients with COVID-19 might also exhibit CNS damage related to the infecting coronavirus. It remains unclear to what extent SARSCoV-2 is able to infect the CNS and, if it does, how the virus reaches the brain, but the possible theories have emerged: spread across the cribriform plate of the ethmoid bone in proximity to the olfactory bulb in patients at the early stage of the disease, resulting in the relatively common loss of sense of smell, or a later-occurring hematogenous spread on the setting of accompanied hypoxia, respiratory, and metabolic acidosis. Direct CNS infection by SARS-CoV has also been shown in mice, but whether SARSCoV-2 infects the brain of humans remains unknown.