The field of metaheuristic optimization has experienced a surge in novel algorithmic developments in recent years, yet there is a lack of consolidated resources focusing on these innovations, especially their categorization and applications in solving real-world problems. This work fills the gap by categorizing and detailing the most recently developed metaheuristic optimization algorithms into local, global, and hybrid methods. The authors explore various optimization algorithms like Runge Kutta Optimization, Manta Ray Foraging Optimization, and Hybrid Marine Predators Algorithm, explaining their mechanisms, pseudocode, and advantages. It also provides case studies to demonstrate their practical applications in fields like supply chain management, robotics, energy optimization, and so on. Thus, the work bridges the gap between theory and application, offering insights that will inspire further innovation and practical implementation of modern optimization techniques.