There exist situations of decision-making under information overload in the Internet, where people have an overwhelming number of available options to choose from, e.g. products to buy in an e-commerce site, or restaurants to visit in a large city. Recommender systems arose as a data-driven personalized decision support tool to assist users in these situations: they are able to process user-related data, filtering and recommending items based on the users preferences, needs and/or behaviour. Unlike most conventional recommender approaches where items are inanimate entities recommended to the users and success is solely determined upon the end users reaction to the recommendation(s) received, in a Reciprocal Recommender System (RRS) users become the item being recommended to other users. Hence, both the end user and the user being recommended should accept the 'matching' recommendation to yield a successful RRS performance. The operation of an RRS entails not only predicting accurate preference estimates upon user interaction data as classical recommenders do, but also calculating mutual compatibility between (pairs of) users, typically by applying fusion processes on unilateral user-to-user preference information. This paper presents a snapshot-style analysis of the extant literature that summarizes the state-of-the-art RRS research to date, focusing on the algorithms, fusion processes and fundamental characteristics of RRS, both inherited from conventional user-to-item recommendation models and those inherent to this emerging family of approaches. Representative RRS models are likewise highlighted. Following this, we discuss the challenges and opportunities for future research on RRSs, with special focus on (i) fusion strategies to account for reciprocity and (ii) emerging application domains related to social recommendation.