arXiv:2408.00166v2 Announce Type: replace-cross Abstract: Explainability of recommender systems has become essential to ensure users' trust and satisfaction. Various types of explainable recommender systems have been proposed including explainable graph-based recommender systems. This review paper discusses state-of-the-art approaches of these systems and categorizes them based on three aspects: learning methods, explaining methods, and explanation types. It also explores the commonly used datasets, explainability evaluation methods, and future directions of this research area. Compared with the existing review papers, this paper focuses on explainability based on graphs and covers the topics required for developing novel explainable graph-based recommender systems.