Abstract: This paper provides a comprehensive review of the evolution of power flow solution methods. Starting with classical approaches such as the Gauss-Seidel and Newton-Raphson methods, the study analyzes their limitations in large-scale systems, particularly in terms of convergence and computational efficiency, and introduces various improvements including acceleration factors, adaptive schemes, and current injection models. To address the growing challenges of high-dimensional and nonlinear systems, recent advancements in artificial intelligence (AI) methods are explored, including neural networks, evolutionary algorithms, and physics-informed neural networks (PINNs), which offer better generalization and adaptability in dynamic environments. Furthermore, the paper highlights the emerging role of quantum algorithms in power flow computation, focusing on hybrid quantum-classical frameworks based on variational quantum algorithms (VQA) and the Harrow-Hassidim-Lloyd (HHL) algorithm. These approaches demonstrate promising potential in improving scalability and accuracy through quantum encoding, circuit construction, and amplitude estimation techniques. The paper concludes by summarizing the features and applicability of each method and provides future perspectives on intelligent, adaptive, and high-performance power flow computation.