Severe acute respiratory syndrome coronavirus‐2 (SARS‐CoV‐2) causes a highly contagious respiratory disease referred to as COVID‐19. However, emerging evidence indicates that a small, but a growing number of COVID‐19 patients also manifest neurological symptoms, suggesting that SARS‐CoV‐2 may infect the nervous system under some circumstances. SARS‐CoV‐2 primarily enters the body through the epithelial lining of the respiratory and gastrointestinal tracts, but under certain conditions this pleiotropic virus may also infect peripheral nerves and gain entry into the central nervous system (CNS). The brain is shielded by various anatomical and physiological barriers, most notably the blood‐brain barrier (BBB) which functions to prevent harmful substances, including pathogens and pro‐inflammatory mediators, from entering the brain. The BBB is composed of highly specialized endothelial cells, pericytes, mast cells and astrocytes that form the neurovascular unit, which regulates BBB permeability and maintains the integrity of the CNS. In this review, we briefly discuss potential routes of viral entry and the possible mechanisms utilized by SARS‐CoV‐2 to penetrate the CNS, either by disrupting the BBB or infecting the peripheral nerves and using the neuronal network to initiate neuroinflammation. Furthermore, we speculate on the long‐term effects of SARS‐CoV‐2 infection on the brain and in the progression of neurodegenerative diseases known to be associated with other human coronaviruses. Although the mechanisms of SARS‐CoV‐2 entry into the CNS and neurovirulence are currently unknown, the potential pathways described here might pave the way for future research in this area and enable the development of better therapeutic strategies.