Fake reviews have become prevalent on various social networks such as e-commerce and social media platforms. As fake reviews cause a heavily negative influence on the public, timely detection and response are of great significance. To this end, effective fake review detection has become an emerging research area that attracts increasing attention from various disciplines like network science, computational social science, and data science. An important line of research in fake review detection is to utilize graph learning methods, which incorporate both the attribute features of reviews and their relationships into the detection process. To further compare these graph learning methods in this paper, we conduct a detailed survey on fake review detection. The survey presents a comprehensive taxonomy and covers advancements in three high-level categories, including fake review detection, fake reviewer detection, and fake review analysis. Different kinds of fake reviews and their corresponding examples are also summarized. Furthermore, we discuss the graph learning methods, including supervised and unsupervised learning approaches for fake review detection. Specifically, we outline the unsupervised learning approach that includes generation-based and contrast-based methods, respectively. In view of the existing problems in the current methods and data, we further discuss some challenges and open issues in this field, including the imperfect data, explainability, model efficiency, and lightweight models.