Coronavirus disease 2019 (COVID-19) is a pandemic disease resulting from severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) infection, primarily in the respiratory tract. This pandemic disease has affected the entire world, and the pathobiology of this disease is not yet completely known. The Interactions of SARS-CoV-2 proteins with different cellular components in the host cell may be necessary for understanding the disease mechanism and identifying crucial pharmacological targets in COVID-19. Studies have suggested that the effect of SARS-CoV-2 on other organs, including the brain, maybe critical for understanding the pathobiology of COVID-19. Symptoms in COVID-19 patients, including impaired consciousness dizziness, headache, loss of taste and smell, vision problems, and neuromuscular pain, suggest that neuronal complications comprise a crucial component of COVID-19 pathobiology. A growing body of literature indicates that SARS-CoV-2 can enter the brain, leading to neuronal defects in COVID-19 patients. Other studies suggest that SARS-CoV-2 may aggravate neuronal complications due to its effects on the cerebrovascular system. Emerging pieces of evidence show that stroke can be one of the leading neurological complications in COVID-19. In this review, we describe the observations about neuronal complications of COVID-19 and how SARS-CoV-2 may invade the brain. We will also discuss the cerebrovascular problems and occurrence of stroke in COVID-19 patients. We will also present the observations and our views about the potential pharmacological strategies and targets in COVID-19. We hope this review will help comprehend the current knowledge of neuronal and cerebrovascular complications from SARS-CoV-2 infections and highlight the possible long-term consequences of SARS-CoV-2 on the human brain.