In December 2019, a new viral disease emerged and quickly spread all around the world. In March 2020, the COVID-19 outbreak was classified as a global pandemic and by June 2021, the number of infected people grew to over 170 million. Along with the patients’ mild-to-severe respiratory symptoms, reports on probable central nervous system (CNS) effects appeared shortly, raising concerns about the possible long-term detrimental effects on human cognition. It remains unresolved whether the neurological symptoms are caused directly by the SARS-CoV-2 infiltration in the brain, indirectly by secondary immune effects of a cytokine storm and antibody overproduction, or as a consequence of systemic hypoxia-mediated microglia activation. In severe COVID-19 cases with impaired lung capacity, hypoxia is an anticipated subsidiary event that can cause progressive and irreversible damage to neurons. To resolve this problem, intensive research is currently ongoing, which seeks to evaluate the SARS-CoV-2 virus’ neuroinvasive potential and the examination of the antibody and autoantibody generation upon infection, as well as the effects of prolonged systemic hypoxia on the CNS. In this review, we summarize the current research on the possible interplay of the SARS-CoV-2 effects on the lung, especially on alveolar macrophages and direct and indirect effects on the brain, with special emphasis on microglia, as a possible culprit of neurological manifestation during COVID-19.