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The development of microgrids is an advantageous option for integrating rapidly growing renewable energies. However, the stochastic nature of renewable energies and variable power demand have created many challenges like unstable voltage/frequency and complicated power management and interaction with the utility grid. Recently, predictive control with its fast transient response and flexibility to accommodate different constraints has presented huge potentials in microgrid applications. This paper provides a comprehensive review of model predictive control (MPC) in individual and interconnected microgrids, including both converter-level and grid-level control strategies applied to three layers of the hierarchical control architecture. This survey shows that MPC is at the beginning of the application in microgrids and that it emerges as a competitive alternative to conventional methods in voltage regulation, frequency control, power flow management and economic operation optimization. Also, some of the most important trends in MPC development have been highlighted and discussed as future perspectives. • A comprehensive review of model predictive control (MPC) in microgrids, including both converter-level and grid-level control strategies applied to three layers of microgrid hierarchical architecture. • Illustrating MPC is at the beginning of the application to microgrids and it emerges as a competitive alternative to conventional methods. • Some of the most important trends in MPC development have been highlighted and discussed as future perspectives. [ABSTRACT FROM AUTHOR]