Animated avatars, which look and talk like humans, are iconic visions of the future of AI-powered systems. Through many sci-fi movies, we are acquainted with the idea of speaking to such virtual personalities as if they were humans. Today, we talk more and more to machines like Apple's Siri, for example, to ask them for the weather forecast. However, when asked for recommendations, for example, for a restaurant to go to, the limitations of such devices quickly become obvious. They do not engage in a conversation to find out what we might prefer, they often do not provide explanations for what they recommend, and they may have difficulties remembering what was said 1 min earlier. Conversational recommender systems (CRS) promise to address these limitations. In this paper, we review existing approaches to building such systems, which developments we observe today, which challenges are still open and why the development of conversational recommenders represents one of the next grand challenges of AI.