While there is abounding literature on virus-induced pathology in general and coronavirus in particular, recent evidence accumulates showing distinct and deleterious brain affection. As the respiratory tract connects to the brain without protection of the blood-brain barrier, SARS-CoV-2 might in the early invasive phase attack the cardiorespiratory centres located in the medulla/pons areas, giving rise to disturbances of respiration and cardiac problems. Furthermore, brainstem regions are at risk to lose their functional integrity. Therefore, long-term neurological as well as psychiatric symptomatology and eventual respective disorders cannot be excluded as evidenced from influenza-A triggered post-encephalitic Parkinsonism and HIV-1 triggered AIDS-dementia complex. From the available evidences for coronavirus-induced brain pathology, this review concludes a number of unmet needs for further research strategies like human postmortem brain analyses. SARS-CoV-2 mirroring experimental animal brain studies, characterization of time-dependent and region-dependent spreading behaviours of coronaviruses, enlightening of pathological mechanisms after coronavirus infection using long-term animal models and clinical observations of patients having had COVID-19 infection are calling to develop both protective strategies and drug discoveries to avoid early and late coronavirus-induced functional brain disturbances, symptoms and eventually disorders. To fight SARS-CoV-2, it is an urgent need to enforce clinical, molecular biological, neurochemical and genetic research including brain-related studies on a worldwide harmonized basis.