The conceptual framework for assessing the situational awareness (SA) of drivers consists of three hierarchical levels: perception of the elements of the environment, comprehension of the elements, and decision-making in the near future. A common challenge in evaluating SA is the determination of the available subjective and objective techniques and their selection and integration into methodologies. Among the objective techniques, eye tracking is commonly used, considering the influence of gaze behavior on driving. This review is presented as an innovative approach to the subject matter, introducing physiological metrics based on eye tracking and investigating their application in assessing the SA of drivers. In addition, experiments and methodologies that revealed patterns at the three levels of SA were identified. For this purpose, databases were searched, and 38 papers were considered. Articles were clustered according to prevalent themes such as eye-tracking metrics, eye-tracking devices, experiment design, and the relationship between SA and eye-tracking. This review summarizes the main metrics and key findings for each article and reveals a wide relationship between the eye-tracking metrics and SA. The influence of appropriately calibrated equipment, refined data collection protocols, and adequate selection of the eye-tracking metrics was examined. Further reviews are needed to systematically collect more evidence.