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Eye gaze analysis is an important research problem in the field of Computer Vision and Human-Computer Interaction. Even with notable progress in the last 10 years, automatic gaze analysis still remains challenging due to the uniqueness of eye appearance, eye-head interplay, occlusion, image quality, and illumination conditions. There are several open questions, including what are the important cues to interpret gaze direction in an unconstrained environment without prior knowledge and how to encode them in real-time. We review the progress across a range of gaze analysis tasks and applications to elucidate these fundamental questions, identify effective methods in gaze analysis, and provide possible future directions. We analyze recent gaze estimation and segmentation methods, especially in the unsupervised and weakly supervised domain, based on their advantages and reported evaluation metrics …