In this paper, we present an extensive survey of music information retrieval (MIR) research into music playlists. Our survey spans more than 20 years, and includes around 300 papers about playlists, with over 70 supporting sources. It is the first survey that is self-contained in the sense that it combines all the different MIR research into playlists. It embraces topics such as algorithms for automatic generation, for automatic continuation, for assisting with manual generation, for tagging and for captioning. It looks at manually constructed playlists, both those that are constructed for and by individuals, and those constructed in collaboration with others. It covers ground-breaking research into enhancing playlists by cross-fading consecutive songs and by interleaving consecutive songs with speech, similar to what happens on a radio show. Most significantly, it is the first survey that can fully incorporate the paradigm shift that has taken place in the way people consume recorded music: the shift from physical media to music streaming. This has wrought profound changes in the size of music collections available to listeners and thus the algorithms that support the construction, curation and presentation of playlists and the methods adopted by users when they also construct, curate and listen to playlists.