Recommender systems are pivotal components of modern Internet platforms and constitute a well-established research field. By now, research has resulted in highly sophisticated recommender algorithms whose further optimization often yields only marginal improvements. This paper goes beyond the commonly dominating focus on optimizing algorithms and instead follows the idea of enhancing recommender systems with reputation data. Since the concept of reputation-enhanced recommender systems has attracted considerable attention in recent years, the main aim of the paper is to provide a comprehensive survey of the approaches proposed so far. To this end, existing work is identified by means of a systematic literature review and classified according to seven carefully considered dimensions. In addition, the resulting structured analysis of the state of the art serves as a basis for the deduction and discussion of several future research directions.