Recent years have witnessed the fast development of the emerging topic of Graph Learning based Recommender Systems (GLRS). GLRS mainly employ advanced graph learning approaches to model users’ preferences and intentions as well as items’ characteristics and popularity for Recommender Systems (RS). Differently from other approaches, including content based filtering and collaborative filtering, GLRS are built on graphs where the important objects, e.g., users, items, and attributes, are either explicitly or implicitly connected. With the rapid development of graph learning techniques, exploring and exploiting homogeneous or heterogeneous relations in graphs is a promising direction for building more effective RS. In this paper, we provide a systematic review of GLRS, by discussing how they extract knowledge from graphs to improve the accuracy, reliability and explainability of the recommendations. First, we characterize and formalize GLRS, and then summarize and categorize the key challenges and main progress in this novel research area.