This chapter introduces the Grey Wolf Optimizer (GWO), a nature-inspired meta-heuristic algorithm that emulates the leadership hierarchy and hunting behaviour of grey wolves in the wild. The algorithm balances exploration and exploitation by modelling alpha, beta, delta, and omega wolves as agents in the search space, with the top three guiding the optimization process. The chapter outlines the social structure and mathematical modelling of GWO, supported by equations and pseudocode. It also presents various modifications to enhance GWO's performance and addresses its limitations in complex, multimodal environments. Applications of GWO in feature selection and neural network training, particularly for classification tasks, are reviewed, showing improved convergence and accuracy compared to traditional algorithms. The chapter concludes by highlighting the value of hybrid or ensemble methods in overcoming GWO’s tendency to get trapped in local minima, setting the stage for further advancements in optimized neural network training.