With the advent of the big data era, clustering algorithms have become pivotal in data mining and machine learning. However, the exponential growth in data size and dimensionality has resulted in escalating time and space complexities for traditional clustering methods, constraining their practical utility. To address these challenges, the anchor point acceleration mechanism has emerged as a potent approach to significantly mitigate computational burdens, thereby augmenting the effectiveness of conventional clustering algorithms for large-scale datasets. This paper provides a comprehensive review of clustering algorithms leveraging the anchor point acceleration mechanism. It explores various techniques such as anchor point generation and the construction of similarity graphs. The discussion encompasses clustering methodologies utilizing fixed anchor pointsq, encompassing spectral clustering, fuzzy spectral clustering, multi-view clustering, and deep clustering algorithms. Additionally, it investigates clustering strategies employing dynamic anchor points, including multi-view and incomplete multi-view clustering algorithms. By synthesizing and analyzing this landscape, the paper identifies current limitations and confronts emerging challenges. It also offers insights into future avenues for advancement, serving as a roadmap for guiding future research and practical applications in the field. This comprehensive examination aims to provide valuable guidance and inspiration to researchers and practitioners alike, fostering continued innovation in clustering algorithms tailored for contemporary data environments.