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With the increasing demand for video-based applications, the reliable prediction of video quality has increased in importance. Numerous video quality assessment methods and metrics have been proposed over the past years with varying computational complexity and accuracy. In this paper, we introduce a classification scheme for full-reference and reduced-reference media-layer objective video quality assessment methods. Our classification scheme first classifies a method according to whether natural visual characteristics or perceptual (human visual system) characteristics are considered. We further subclassify natural visual characteristics methods into methods based on natural visual statistics or natural visual features. We subclassify perceptual characteristics methods into frequency or pixel-domain methods. According to our classification scheme, we comprehensively review and compare the media-layer objective video quality models for both standard resolution and high definition video. We find that the natural visual statistics based MultiScale-Structural SIMilarity index (MS-SSIM), the natural visual feature based Video Quality Metric (VQM), and the perceptual spatio-temporal frequency-domain based MOtion-based Video Integrity Evaluation (MOVIE) index give the best performance for the LIVE Video Quality Database.