Reduced-reference (RR) video-quality estimators send a small signature to the receiver. This signature comprises the original video content as well as the video stream. RR quality estimation provides reliability and involves a small data payload. While significant in theory, RR estimators have only recently been used in practice for quality monitoring and adaptive system control in streaming-video frameworks. In this paper, we classify RR algorithms according to whether they are based on a) modeling the signal distortion, b) modeling the human visual system, or c) analyzing the video signal source. We review proposed RR techniques for monitoring and controlling quality in streaming video systems.