With confirmed coronavirus disease 2019 (COVID-19) cases surpassing the 18 million mark around the globe, there is an imperative need to gain comprehensive understanding of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Although the main clinical manifestations of COVID-19 are associated with respiratory or intestinal symptoms, reports of neurological signs and symptoms are increasing. The etiology of these neurological manifestations remains obscure, and probably involves several direct pathways, not excluding the direct entry of the virus to the central nervous system (CNS) through the olfactory epithelium, circumventricular organs, or disrupted blood–brain barrier. Furthermore, neuroinflammation might occur in response to the strong systemic cytokine storm described for COVID-19, or due to dysregulation of the CNS rennin-angiotensin system. Descriptions of neurological manifestations in patients in the previous coronavirus (CoV) outbreaks have been numerous for the SARS-CoV and lesser for Middle East respiratory syndrome coronavirus (MERS-CoV). Strong evidence from patients and experimental models suggests that some human variants of CoV have the ability to reach the CNS and that neurons, astrocytes, and/or microglia can be target cells for CoV. A growing body of evidence shows that astrocytes and microglia have a major role in neuroinflammation, responding to local CNS inflammation and/or to disbalanced peripheral inflammation. This is another potential mechanism for SARS-CoV-2 damage to the CNS. In this comprehensive review, we will summarize the known neurological manifestations of SARS-CoV-2, SARS-CoV and MERS-CoV; explore the potential role for astrocytes and microglia in the infection and neuroinflammation; and compare them with the previously described human and animal CoV that showed neurotropism to propose possible underlying mechanisms.