Microgrids face significant challenges due to the unpredictability of distributed generation (DG) technologies and fluctuating load demands. These challenges result in complex power management systems characterised by voltage/frequency variations and intricate interactions with the utility grid. Model predictive control (MPC) has emerged as a powerful technique to effectively address these challenges. By applying a receding horizon control strategy, MPC offers promising solutions for optimising constraints and enhancing microgrid operations. The purpose of this review paper is to comprehensively analyse the application of MPC in microgrids, covering various levels of the hierarchical control structure. Furthermore, this paper explores the emerging trend of employing MPC across microgrid applications, ranging from converter control levels for power quality to overarching energy management systems. It also investigates the future research perspectives by considering the challenges associated with establishing MPC-based microgrid control. The key conclusion derived from this review paper is that the implementation of MPC techniques in microgrid operations can greatly improve their overall performance, efficiency, and resilience. This paper thoroughly examines the various challenges faced in MPC-based microgrid operations, underscoring the significance of conducting research in advanced artificial intelligence (AI)-based MPC methods. It highlights how these cutting-edge AI techniques can bring about economic benefits in microgrid operations, addressing the complex demands of efficient energy management in a rapidly evolving landscape. The presented insights strive to enhance the comprehension and adoption of MPC techniques in microgrid settings, actively contributing to the ongoing improvement of their operational processes. By shedding light on key aspects and offering valuable guidance, this work aims to propel the advancement and effective utilisation of MPC methodologies in microgrids, ultimately leading to optimised performance and enhanced overall operations.