In the field of data mining, clustering has shown to be an important technique. Numerous clustering methods have been devised and put into practice, and most of them locate high-quality or optimum clustering outcomes in the field of computer science, data science, statistics, pattern recognition, artificial intelligence, and machine learning. This research provides a modern, thorough review of both classic and cutting-edge clustering methods. The taxonomy of clustering is presented in this review from an applied angle and the compression of some hierarchical and partitional clustering algorithms with various parameters. We also discuss the open challenges in clustering such as computational complexity, refinement of clusters, speed of convergence, data dimensionality, effectiveness and scalability, data object representation, evaluation measures, data streams, and knowledge extraction; scientists and professionals alike will be able to use it as a benchmark as they strive to advance the state-of-the-art in clustering techniques. © 2023 by the authors.