Numerous investigations have demonstrated significant and long-lasting neurological manifestations of COVID-19. It has been suggested that as many as four out of five patients who sustained COVID-19 will show one or several neurological symptoms that can last months after the infection has run its course. Neurological symptoms are most common in people who are less than 60 years of age, while encephalopathy is more common in those over 60. Biological mechanisms for these neurological symptoms need to be investigated and may include both direct and indirect effects of the virus on the brain and spinal cord. Individuals with Alzheimer’s disease (AD) and related dementia, as well as persons with Down syndrome (DS), are especially vulnerable to COVID-19, but the biological reasons for this are not clear. Investigating the neurological consequences of COVID-19 is an urgent emerging medical need, since close to 700 million people worldwide have now had COVID-19 at least once. It is likely that there will be a new burden on healthcare and the economy dealing with the long-term neurological consequences of severe SARS-CoV-2 infections and long COVID, even in younger generations. Interestingly, neurological symptoms after an acute infection are strikingly similar to the symptoms observed after a mild traumatic brain injury (mTBI) or concussion, including dizziness, balance issues, anosmia, and headaches. The possible convergence of biological pathways involved in both will be discussed. The current review is focused on the most commonly described neurological symptoms, as well as the possible molecular mechanisms involved.