Drowsiness in drivers has become a serious cause of concern due to the occurrences of a large number of fatalities on the road each year. Lives of pedestrians and passengers are put to risk as drivers tend to fall asleep at the steering wheel. In the recent past, many researchers have paid attention to the problem of drowsiness detection since safe roads and safe driving are of paramount concern to all societies. This paper has led to the development of several novel and effective methods in detecting drivers' drowsiness. These include: 1) Vehicle based methods; 2) Behavioral methods; and 3) Physiological methods. Since wake-sleep is an intermediate state between two physiologically dissimilar states, physiological signals can define this transition more accurately when compared with approaches that fall in other categories. This paper focuses on the role of physiological signals in detecting driver's drowsiness level. The proposed methods measure the physiological signals by means of various sensors, which monitor the driver's physiological parameters on a continual basis. Multiple sensors can be embedded on the driver or in the vicinity of the driver to capture vital signs indicating the onset of drowsiness. The aim here is to provide an insightful review of all such key approaches that fall in this category. This paper conducts a detailed study in which key physiological parameters that relate to drowsiness are identified, described, and analyzed. Furthermore, the overall advantages and limitations of these physiological based schemes are also highlighted.