Recommender systems are software applications that help users to find items of interest in situations of information overload. Current research often assumes a one-shot interaction paradigm, where the users' preferences are estimated based on past observed behavior and where the presentation of a ranked list of suggestions is the main, one-directional form of user interaction. Conversational recommender systems (CRS) take a different approach and support a richer set of interactions. These interactions can, for example, help to improve the preference elicitation process or allow the user to ask questions about the recommendations and to give feedback. The interest in CRS has significantly increased in the past few years. This development is mainly due to the significant progress in the area of natural language processing, the emergence of new voice-controlled home assistants, and the increased use of chatbot technology. With this paper, we provide a detailed survey of existing approaches to conversational recommendation. We categorize these approaches in various dimensions, e.g., in terms of the supported user intents or the knowledge they use in the background. Moreover, we discuss technological approaches, review how CRS are evaluated, and finally identify a number of gaps that deserve more research in the future. CCS Concepts: • Information systems → Recommender systems; • General and reference → Surveys and overviews; • Human-centered computing → Interactive systems and tools;