Adaptive control, smart grid, power electronics, grid-connected inverter, microgrid, reinforcement learning, model predictive control, neural networks, renewable energy integration, power quality. The rapid transition toward smart grids has fundamentally transformed the architecture and operational dynamics of modern power systems. The integration of renewable energy sources, distributed generation, and power electronic converters introduces nonlinearities, uncertainties, and time-varying dynamics that challenge conventional control strategies. Adaptive control techniques have emerged as a critical solution to ensure system stability, robustness, and real-time optimization in such complex environments. This paper presents a comprehensive investigation of adaptive control methodologies applied to power electronics in smart grid systems. It examines model reference adaptive control (MRAC), adaptive predictive control, sliding mode control, neural network-based adaptive systems, and reinforcement learning-driven control strategies. The study further evaluates their applications in grid-connected converters, microgrids, energy storage systems, and voltage frequency regulation. Two analytical tables are included to compare control strategies and application-specific performance metrics. The paper also highlights recent developments (2022– 2024), including data-driven and AI-integrated adaptive control frameworks. Finally, key challenges such as cyber-security, computational complexity, and scalability are discussed, followed by future research directions focusing on hybrid intelligent control systems.