Drowsiness is not only a core challenge to safe driving in traditional driving conditions but also a serious obstacle for the wide acceptance of added services of self-driving cars (because drowsiness is, in fact, one of the most representative early-stage symptoms of self-driving carsickness). In view of the importance of detecting drivers’ drowsiness, this paper reviews the algorithms of electroencephalogram (EEG)-based drivers’ drowsiness detection (DDD). To facilitate the review, the EEG-based DDD approaches are organized into a tree structure taxonomy, having two main categories, namely “detection only (open-loop)” and “management (closed-loop)”, both aimed at designing better DDD systems that ensure early detection, reliability and practical utility. To achieve this goal, we addressed seven questions, the answers of which helped in developing an EEG-based DDD system that is superior to the existing ones. A basic assumption in this review article is that although driver drowsiness and carsickness-induced drowsiness are caused by different factors, the brain network that regulates drowsiness is the same.