Neuromorphic vision sensors, commonly referred to as Event Cameras (ECs), have gained prominence as a field of research in Computer Vision. This popularity stems from the numerous unique characteristics including High Dynamic Range, High Temporal Resolution, and Low Latency. Of particular interest is their temporal resolution, which proves ideal for human monitoring applications. Capturing rapid facial movements and eye gaze can be effectively achieved with ECs. Recent studies involving the use of ECs for object detection and tracking have demonstrated success in tasks involving Eye Motion Analysis such as Eye tracking, Blink detection, Gaze estimation and Pupil tracking. The objective of this study is to provide a comprehensive review of the current research in the aforementioned tasks, focusing on the potential utilization of ECs for future tasks involving rapid eye motion detection, such as detection and classification of saccades. We highlight studies that may serve as a foundation for undertaking such a task, such as pupil tracking and gaze estimation. We also highlight in our review some common challenges encountered such as the availability of datasets and review some of the methods used in solving this problem. Finally, we discuss some limitations of this field of research and conclude with future directions including real-world applications and potential research directions.