Most SARS CoV-2 infections probably occur unnoticed or cause only cause a mild common cold that does not require medical intervention. A significant proportion of more severe cases is characterized by early neurological symptoms such as headache, fatigue, and impaired consciousness, including respiratory distress. These symptoms suggest hypoxia, specifically affecting the brain. The condition is best explained by primary replication of the virus in the nasal respiratory and/or the olfactory epithelia, followed by an invasion of the virus into the central nervous system, including the respiratory centers, either along a transneural route, through disruption of the blood-brain barrier, or both. In patients, presenting with early dyspnea, the primary goal of therapy should be the reversal of brain hypoxia as efficiently as possible. The first approach should be intermittent treatment with 100% oxygen using a tight oronasal mask or a hood. If this does not help within a few hours, an enclosure is needed to increase the ambient pressure. This management approach is well established in the hypoxia-related diseases in diving and aerospace medicine and preserves the patient's spontaneous breathing. Preliminary research evidence indicates that even a small elevation of the ambient pressure might be lifesaving. Other neurological symptoms, presenting particularly in long COVID-19, suggest imbalance of the autonomous nervous system, i.e., dysautonomia. These patients could benefit from vagal nerve stimulation.