The recommendation of food items is important for many reasons. Attaining cooking inspiration via digital sources is becoming evermore popular; as are systems, which recommend other types of food, such as meals in restaurants or products in supermarkets. Researchers have been studying these kinds of systems for many years, suggesting not only that can they be a means to help people find food they might want to eat, but also help them nourish themselves more healthily. This paper provides a summary of the state-of-the-art of so-called food recommender systems, highlighting both seminal and most recent approaches to the problem, as well as important specializations, such as food recommendation systems for groups of users or systems which promote healthy eating. We moreover discuss the diverse challenges involved in designing recsys for food, summarise the lessons learned from past research and outline what we believe to be important future directions and open questions for the field. In providing these contributions we hope to provide a useful resource for researchers and practitioners alike.