<p>The Runge Kutta Optimizer (RUN) is a mathematics-based metaheuristic algorithm (MA) designed by utilizing the principles of slope variations calculated by the Runge Kutta (RK) technique as an effective and rational search mechanism for global optimization. RUN was developed in 2021 and quickly garnered recognition in the academic field for its strong efficiency and versatility. The algorithm is faster, more accurate at convergent operations, and better at solving problems overall, making it a strong competitor to existing MAs. This study offers a thorough overview of RUN, examining the different versions and variations published in several research papers since its beginning in 2021, with 94% published in reputable peer-reviewed journals and 6% in international conference proceedings. This study addresses variants of RUN, comprising 77% of the improved version of RUN, 14% of hybridization, 3% of binary, and 3% of multi-objective variants, respectively. Moreover, the applications of RUN demonstrate its efficacy and versatility across several domains, with 45% in power and control engineering, 25% in machine learning, 21% in benchmark functions and engineering design challenges, and 5% in feature selection. The algorithm has been extensively employed in the fields of image processing and cloud computing. This paper aims to provide a comprehensive review of RUN, examining its theoretical framework, analytical methods, enhancement tactics, and practical applications across many optimization domains. Furthermore, we also evaluate the RUN’s performance in partitional clustering for digital pathology image segmentation to demonstrate its efficiency. Experimental results show that the RUN-based clustering model produces the best segmentation results compared to the other five tested MA-based clustering models as per reference and ground truth-based quality metrics. The run-based model provides over 92% segmentation accuracy with the third-lowest execution time.</p>