Metaheuristic optimization methods, widely used in applications ranging from machine learning to optimal control, often lack a rigorous mathematical foundation. Many of these approaches are driven by stochastic particle systems and rely on heuristic techniques that are challenging to analyze formally. Recently, tools from statistical physics have offered a new perspective on metaheuristic algorithms through partial differential equations (PDEs), particularly kinetic and mean-field PDEs. This approach provides a foundation for developing a robust mathematical theory of convergence to the global minimum and opens up opportunities for systematically enhancing algorithm performance. In this talk, we will explore popular metaheuristic algorithms, such as simulated annealing, genetic algorithms, and particle swarm optimization, by showing how, in the limit of large particle numbers, these algorithms can be described by kinetic equations. We will also discuss connections to other optimization approaches, including Langevin dynamics and consensus-based optimization, and highlight several illustrative applications.