<p>The Mapper algorithm is a topological data analysis (TDA) technique that constructs simplified representations of high-dimensional data as graphs to uncover underlying structural patterns. The algorithm has attracted significant attention from researchers and has been applied across various disciplines. However, to the best of the authors’ knowledge, there is currently no comprehensive review of the Mapper algorithm and its variants in terms of their application across various fields between 2007 and 2025. This review addresses this gap and aims to contribute as a valuable resource for researchers and practitioners who intend to explore or utilize the algorithm. The reviewed literature comprises articles retrieved from major academic databases, including Google Scholar, Web of Science, Scopus, JSTOR, PubMed, and IEEE Xplore, using the keywords “topological data analysis,” “Mapper algorithm,” and “topological graph” in the search process. The study further provides an overview and a comparative analysis of the suitability of the most used filter functions and clustering algorithms within the Mapper framework. Additionally, it examines current trends, identifies limitations, and proposes future research directions for the Mapper algorithm and its variants, emphasizing the need to develop effective methodologies for the analysis of high-dimensional data in the era of enormous data proliferation.</p>