Research on event-based processing and analysis of media is receiving an increasing attention from the scientific community due to its relevance for an abundance of applications, from consumer video management and video surveillance to lifelogging and social media. Events have the ability to semantically encode relationships of different informational modalities, such as visual-audio-text, time, involved agents and objects, with the spatio-temporal component of events being a key feature for contextual analysis. This unveils an enormous potential for exploiting new information sources and opening new research directions. In this paper, we survey the existing literature in this field. We extensively review the employed conceptualization of the notion of event in multimedia, the techniques for event representation and modeling, the feature representation and event inference approaches for the problems of event detection in audio, visual, and textual content. Furthermore, we review some key event-based multimedia applications, and various benchmarking activities that provide solid frameworks for measuring the performance of different event processing and analysis systems. We provide an in-depth discussion of the insights obtained from reviewing the literature and identify future directions and challenges.