Graph clustering methods are popular due to their ability to discover clusters with arbitrary shapes. However, with the emergence of large-scale datasets, the efficiency of graph clustering algorithms has become a significant concern. As a result, many researchers have been drawn to the field of fast graph clustering algorithms, leading to rapid and intricate advancements in related research. Nevertheless, there is currently no comprehensive survey available for fast graph clustering algorithms. To address this gap, we review these fast graph clustering models in both single and multi-view fields, categorizing them based on different properties and analyzing their advantages and disadvantages. In the single-view field, the main categories we explore include large graph methods and bipartite graph methods. The former includes graph cut and graph density methods, while the latter includes graph cut, co-clustering, and label transmission methods. For the multi-view field, the main categories also include large graph methods and bipartite graph methods. The former is specifically designed to avoid the eigenvalue decomposition of graph cut models, and the latter focuses on accelerating algorithms by integrating anchor points. Towards the conclusion of this paper, we discuss the challenges and provide several further research directions for fast graph clustering.