This article provides a comprehensive review of the application of Model Predictive Control (MPC) in power electronics, highlighting its advantages and challenges. MPC, known for its ability to handle multivariable systems and nonlinearities, has gained significant attention due to its effectiveness in various applications such as active front ends (AFE), power converters with RL loads, inverters with LC filters, and high-performance drives for induction machines. The article discusses the theoretical foundations of MPC, including the use of system models to predict future behavior and optimize control actions. It also explores different MPC techniques, such as finite-control-set MPC (FCS-MPC) and generalized predictive control (GPC), and their implementation in power electronics. The authors analyze research trends from 2007 to 2012, showing that grid-connected converters and high-performance drives are the most studied areas. The article further delves into specific applications, including the control of AFEs, active filters, matrix converters, multilevel inverters, and high-performance drives, providing detailed examples and experimental results. Finally, it addresses future challenges, such as improving model accuracy, reducing computational complexity, and developing analytical tools for performance evaluation.This article provides a comprehensive review of the application of Model Predictive Control (MPC) in power electronics, highlighting its advantages and challenges. MPC, known for its ability to handle multivariable systems and nonlinearities, has gained significant attention due to its effectiveness in various applications such as active front ends (AFE), power converters with RL loads, inverters with LC filters, and high-performance drives for induction machines. The article discusses the theoretical foundations of MPC, including the use of system models to predict future behavior and optimize control actions. It also explores different MPC techniques, such as finite-control-set MPC (FCS-MPC) and generalized predictive control (GPC), and their implementation in power electronics. The authors analyze research trends from 2007 to 2012, showing that grid-connected converters and high-performance drives are the most studied areas. The article further delves into specific applications, including the control of AFEs, active filters, matrix converters, multilevel inverters, and high-performance drives, providing detailed examples and experimental results. Finally, it addresses future challenges, such as improving model accuracy, reducing computational complexity, and developing analytical tools for performance evaluation.