This article provides a tutorial overview of current approaches for monitoring the quality perceived by users of IP-based audiovisual media services. The article addresses both mobile and fixed network services such as mobile TV or Internet Protocol TV (IPTV). It reviews the different quality models that exploit packet- header-, bit stream-, or signal-information for providing audio, video, and audiovisual quality estimates, respectively. It describes how these models can be applied for real-life monitoring, and how they can be adapted to reflect the information available at the given measurement point. An outlook gives insight into emerging trends for near- and mid-term future requirements and solutions.