Residual excessive daytime sleepiness (REDS) in patients with obstructive sleep apnea is characterized by persisting sleepiness despite effective and standardized therapies. Compared to patients without REDS, these patients seem to have specific characteristics such as initially increased Epworth Sleepiness Scale (ESS) scores, more comorbidities, altered brain structures, and neurochemical changes in brain regions responsible for sleep-wake regulation, emotion, motor skills, and cognition. Patients with REDS must undergo thorough evaluation of differential diagnoses, therapeutic procedures, and comorbidities over a period of about 3 months, with the possibility of changing therapeutic interventions and treatment of factors causing sleepiness. Only if all these procedures fail to improve REDS can drug therapy with wakefulness-promoting agents be indicated to prevent possible irreversible changes of brain structures.