Driver drowsiness is a major cause of fatal traffic accidents. Automated driving might counteract this problem in the end by taking over more and more the driving task and reducing human-made errors in this way. However, in the lower levels of automation, the driver is still responsible as a fallback authority. Consequently, systems for the reliable monitoring and detection of the driver's current state, especially regarding the risk factor drowsiness, are required. Current commercial drowsiness detection systems mainly focus on the analysis of driving-related parameters. These parameters cannot be evaluated to the usual extent in the ongoing automation of the driving task since the automated system controls the vehicle more and more. Especially techniques that include physiological measurements seem to be a promising alternative. However, in a dynamic environment such as driving, only non- or minimal intrusive methods are accepted, and vibrations from the roadbed could lead to degraded sensor technology. A solution for the mentioned problems could be integrating consumer-grade smart wearables in the vehicle. Besides, existing vehicles could quickly be upgraded and retrofitted with this technology without installing additional sensors. For this reason and encouraged by the ongoing progress in the development of smart wearable devices in recent years, this work investigated the potential of applying their recorded physiological data in an automotive environment. Experimental results from three user studies prove the potential and feasibility of driver drowsiness detection based on physiological data from smart wearables. Several aspects and open challenges in driver drowsiness detection are highlighted that need to be considered in further research. Thereby, the knowledge gained in this work can serve as a starting point and provide incentives for researchers and automobile manufacturers for novel and intelligent driver-vehicle interaction concepts for driver state monitoring on the way to full driving automation. Safety on the roads needs to be further increased by reducing fatal accidents based on risk factors such as driver drowsiness.