In the last decade, drowsiness while driving has been identified as a major factor behind a large number of fatal traffic accidents around the world. This highly prevalent problem has caused significant loss of life, injuries, property damage, and economic losses in many parts of the world. For that, great efforts have been made to introduce driver’s drowsiness detection systems for reducing and preventing traffic accidents in many cities in the world. Among the existing driver assistance systems, the one based on the EEG signal measurement is the most popular and relevant system. Nevertheless, EEG signals can be easily altered by many kinds of artifacts arising from sources other than the brain, such as muscle (EMG), cardiac (ECG), and ocular (EOG) activities. In the midst of them, ocular artifacts are one of the most important noise sources among the others. In this paper, we give an in-depth review on techniques used to detect and eliminate ocular artifacts from EEG recordings for all potential EEG-based drowsiness warning applications. Initially, we present an overview of some significant artifact types that can be observed in EEG signals and we study their impact on drowsiness detection applications. Subsequently, we review many approaches to artifact rejection, categorize and compare them based on their ability to eliminate EOG artifacts. Finally, we provide an innovative idea based on the IoT Cloud, which might be the succeeding step for safe driving, for alerting the driver when is getting drowsy.