This review discusses the computational challenges and breakthroughs in large-scale photonic inverse design, focusing on the optimization of all geometrical degrees of freedom. It highlights the need for efficient electromagnetic solvers and advanced optimization techniques to address the computational demands of designing large-scale photonic structures. The review covers various electromagnetic solvers, including conventional methods like the finite element method (FEM), finite-difference time-domain (FDTD), and rigorous coupled-wave analysis (RCWA), as well as neural network-based solvers. It also explores optimization techniques such as evolutionary algorithms, gradient-based methods, and machine learning approaches. The article emphasizes the importance of hardware acceleration and parallel computing to overcome computational bottlenecks, particularly in large-scale simulations. Additionally, it discusses the integration of deep learning models to approximate Maxwell's equations, reducing computational overhead. The review aims to provide insights into navigating the landscape of large-scale photonic design and advocates for strategic advancements in optimization methods, solver selection, and the integration of neural networks to overcome computational barriers.This review discusses the computational challenges and breakthroughs in large-scale photonic inverse design, focusing on the optimization of all geometrical degrees of freedom. It highlights the need for efficient electromagnetic solvers and advanced optimization techniques to address the computational demands of designing large-scale photonic structures. The review covers various electromagnetic solvers, including conventional methods like the finite element method (FEM), finite-difference time-domain (FDTD), and rigorous coupled-wave analysis (RCWA), as well as neural network-based solvers. It also explores optimization techniques such as evolutionary algorithms, gradient-based methods, and machine learning approaches. The article emphasizes the importance of hardware acceleration and parallel computing to overcome computational bottlenecks, particularly in large-scale simulations. Additionally, it discusses the integration of deep learning models to approximate Maxwell's equations, reducing computational overhead. The review aims to provide insights into navigating the landscape of large-scale photonic design and advocates for strategic advancements in optimization methods, solver selection, and the integration of neural networks to overcome computational barriers.