Increasing evidence suggests that Severe Acute Respiratory Syndrome-coronavirus-2 (SARS-CoV-2) can also invade the central nervous system (CNS). However, findings available on its neurological manifestations and their pathogenic mechanisms have not yet been systematically addressed. A literature search on neurological complications reported in patients with COVID-19 until June 2020 produced a total of 23 studies. Overall, these papers report that patients may exhibit a wide range of neurological manifestations, including encephalopathy, encephalitis, seizures, cerebrovascular events, acute polyneuropathy, headache, hypogeusia, and hyposmia, as well as some non-specific symptoms. Whether these features can be an indirect and unspecific consequence of the pulmonary disease or a generalized inflammatory state on the CNS remains to be determined; also, they may rather reflect direct SARS-CoV-2-related neuronal damage. Hematogenous versus transsynaptic propagation, the role of the angiotensin II converting enzyme receptor-2, the spread across the blood-brain barrier, the impact of the hyperimmune response (the so-called "cytokine storm"), and the possibility of virus persistence within some CNS resident cells are still debated. The different levels and severity of neurotropism and neurovirulence in patients with COVID-19 might be explained by a combination of viral and host factors and by their interaction.