Model-predictive control (MPC) has emerged as a promising control method in power electronics, particularly for multiobjective control problems such as multilevel inverter (MLI) applications. Over the past two decades, improving the performance of MPC and tackling its technical challenges, such as computational load, modeling accuracy, cost function design, and weighting factor selection, have attracted great interest in power electronics. This article aims to discuss the current state of MPC strategies for MLI applications, describing the significance of each challenge with the reported effective solutions. Through this review, the MPC methods are categorized into two groups: direct MPC (without modulator) and indirect MPC (with modulator). The recent advances of each category are presented and analyzed, focusing on direct MPC as the most applied method for MLI topologies. In addition, some of the important concepts are experimentally validated through a case study and compared under the same operating conditions to evaluate the performance and highlight their features. Finally, the future trends of MPC for MLI applications are discussed based on the current state and reported developments.