Graph mining algorithms have been playing a significant role in myriad fields over the years. However, despite their promising performance on various graph analytical tasks, most of these algorithms lack fairness considerations. As a consequence, they could lead to discrimination towards certain populations when exploited in human-centered applications. Recently, algorithmic fairness has been extensively studied in graph-based applications. In contrast to algorithmic fairness on independent and identically distributed (i.i.d.) data, fairness in graph mining has exclusive backgrounds, taxonomies, and fulfilling techniques. In this survey, we provide a comprehensive and up-to-date introduction of existing literature under the context of fair graph mining. Specifically, we propose a novel taxonomy of fairness notions on graphs, which sheds light on their connections and differences. We further present an organized summary of existing techniques that promote fairness in graph mining. Finally, we summarize the widely used datasets in this emerging research field and provide insights on current research challenges and open questions, aiming at encouraging cross-breeding ideas and further advances.