<p>This study comprehensively reviews model predictive control (MPC) strategies for power converters in microgrids across primary, secondary, and tertiary control levels. Key developments include the integration of artificial intelligence (AI) with MPC to enhance dynamic response and uncertainty handling, particularly through data-driven approaches, which optimize the cost function. The control framework is further refined into AI-based MPC to address challenges such as topology diversity, high photovoltaic penetration, and switching dynamics. Digital twin technology establishes bidirectional mapping between the physical and cyber spaces to support real-time optimization. By combining situational awareness, cloud computing, and AI-driven forecasting, adaptive and self-optimizing microgrid operation is facilitated. However, the increasing complexity of modern microgrids—driven by source-load uncertainty and limited resource flexibility—demands a shift from conventional model-driven methods to a data-physical fusion paradigm. Finally, future research directions are outlined, which highlight the integration of scalable AI-based MPC and the standardization of digital twin technologies.</p>