Under the explosive growth of information available on the Web, recommender systems have been used as an effective technology to filter useless information and attempt to recommend the most useful items. The proliferation of smart phones, smart wearable devices and other Internet of Thing (IoT) devices has gradually driven many novel emerging services which are latency-sensitive and computation-intensive with a higher quality-of-service. Under such circumstances, the data sources contain four key characteristics (i.e., sparsity, heterogeneity, mobility, volatility). The conventional recommender systems based on cloud computing are incapable of digging the information of user demands. Mobile edge computing is a novel computing paradigm via pushing computation/storage resource from the remote cloud servers to the network edge servers to provide more intelligent and personalized service. This paper comprehensively reviews the state of the art literature on the convergence of recommender systems and edge computing, and identify the future directions along this dimension. This paper can provide an array of new perspectives on the convergence for researchers, practitioners, and tap into the richness of this interdisciplinary research area.