This paper investigates the problem of assessing the quality of video transmitted over IP networks. Our goal is to develop a methodology that is both reasonably accurate and simple enough to support the large-scale deployments that the increasing use of video over IP are likely to demand. For that purpose, we focus on developing an approach that is capable of mapping network statistics, e.g., packet losses, available from simple measurements, to the quality of video sequences reconstructed by receivers. A first step in that direction is a loss-distortion model that accounts for the impact of network losses on video quality, as a function of application-specific parameters such as video codec, loss recovery technique, coded bit rate, packetization, video characteristics, etc. The model, although accurate, is poorly suited to large-scale, on-line monitoring, because of its dependency on parameters that are difficult to estimate in real-time. As a result, we introduce a "relative quality" metric (rPSNR) that bypasses this problem by measuring video quality against a quality benchmark that the network is expected to provide. The approach offers a lightweight video quality monitoring solution that is suitable for large-scale deployments. We assess its feasibility and accuracy through extensive simulations and experiments.