With the progression of investigations on the pathogenesis of severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2), neurological complications have emerged as a critical aspect of the ongoing coronavirus disease 2019 (Covid‐19) pandemic. Besides the well‐known respiratory symptoms, many neurological manifestations such as anosmia/ageusia, headaches, dizziness, seizures, and strokes have been documented in hospitalised patients. The neurotropism background of coronaviruses has led to speculation that the neurological complications are caused by the direct invasion of SARS‐CoV‐2 into the nervous system. This invasion is proposed to occur through the infection of peripheral nerves or via systemic blood circulation, termed neuronal and haematogenous routes of invasion, respectively. On the other hand, aberrant immune responses and respiratory insufficiency associated with Covid‐19 are suggested to affect the nervous system indirectly. Deleterious roles of cytokine storm and hypoxic conditions in blood‐brain barrier disruption, coagulation abnormalities, and autoimmune neuropathies are well investigated in coronavirus infections, as well as Covid‐19. Here, we review the latest discoveries focussing on possible molecular mechanisms of direct and indirect impacts of SARS‐CoV‐2 on the nervous system and try to elucidate the link between some potential therapeutic strategies and the molecular pathways.