Advances in power electronics and digital control open a new horizon in the control of power converters. Particularly, model predictive control has been developed for control applications in industrial electronics and power systems. This study presents a comprehensive study on recent achievements of model predictive control algorithms to overcome the challenges in the real-time implementation of power converter control, which is the lowest level control of hierarchical control in microgrids. The study shows that most of these alternate solutions can enhance system reliability, stability, and efficiency. The control platform devices for the real-time implementation of these algorithms are compared. The related issues are discussed and classified, respectively. Finally, a summary is provided, leading to some further research questions and future work.