Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) invades human cells by binding to the angiotensin-converting-enzyme-2 (ACE-2) using a spike protein and leads to Coronavirus disease-2019 (COVID-19). COVID-19 primarily causes a respiratory infection that can lead to severe systemic inflammation. It is also common for some patients to develop significant neurological and psychiatric symptoms. The spread of SARS-CoV-2 to the CNS likely occurs through several pathways. Once spread in the CNS, many acute symptoms emerge, and such infections could also transpire into severe neurological complications, including encephalitis or ischemic stroke. After recovery from the acute infection, a significant percentage of patients develop "long COVID," a condition in which several symptoms of COVID-19 persist for prolonged periods. This review aims to discuss acute and chronic neurological problems after SARS-CoV-2 infection. The potential mechanisms by which SARS-CoV-2 enters the CNS and causes neuroinflammation, neuropathological changes observed in post-mortem brains of COVID-19 patients, and cognitive and mood problems in COVID-19 survivors are discussed in the initial part. The later part of the review deliberates the causes of long COVID, approaches for noninvasive tracking of neuroinflammation in long COVID patients, and the potential therapeutic strategies that could ease enduring CNS symptoms observed in long COVID.