The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) is the causative pathogen of the coronavirus disease 2019 (COVID-19) pandemic, a fatal respiratory illness. The associated risk factors for COVID-19 are old age and medical comorbidities. In the current combined antiretroviral therapy (cART) era, a significant portion of people living with HIV-1 (PLWH) with controlled viremia is older and with comorbidities, making these people vulnerable to SARS-CoV-2 infection and COVID-19-associated severe outcomes. Additionally, SARS-CoV-2 is neurotropic and causes neurological complications, resulting in a health burden and an adverse impact on PLWH and exacerbating HIV-1-associated neurocognitive disorder (HAND). The impact of SARS-CoV-2 infection and COVID-19 severity on neuroinflammation, the development of HAND and preexisting HAND is poorly explored. In the present review, we compiled the current knowledge of differences and similarities between SARS-CoV-2 and HIV-1, the conditions of the SARS-CoV-2/COVID-19 and HIV-1/AIDS syndemic and their impact on the central nervous system (CNS). Risk factors of COVID-19 on PLWH and neurological manifestations, inflammatory mechanisms leading to the neurological syndrome, the development of HAND, and its influence on preexisting HAND are also discussed. Finally, we have reviewed the challenges of the present syndemic on the world population, with a particular emphasis on PLWH.