The modular multilevel matrix converter is a relatively new power converter topology suitable for high-power alternating current (AC)-to-AC applications. Several publications in the literature have highlighted the converter capabilities, such as full modularity, fault-redundancy, control flexibility and input/output power quality. However, the topology and control of this converter are relatively complex to realise, considering that the converter has a large number of power-cells and floating capacitors. To the best of the authors' knowledge, there are no review papers where the applications of the modular multilevel matrix converter are discussed. Hence, this paper aims to provide a comprehensive review of the state-of-the-art of the modular multilevel matrix converter, focusing on implementation issues and applications. Guidelines to dimensioning the key components of this converter are described and compared to other modular multilevel topologies, highlighting the versatility and controllability of the converter in high-power applications. Additionally, the most popular applications for the modular multilevel matrix converter, such as wind turbines, grid connection and motor drives, are discussed based on analyses of simulation and experimental results. Finally, future trends and new opportunities for the use of the modular multilevel matrix converter in high-power AC-to-AC applications are identified.