The Modular Multilevel Matrix Converter is a relatively new power converter topology appropriate for high-power Alternating Current (AC) to AC purposes. Several publications in the literature have highlighted the converter capabilities such as modularity, control flexibility, the possibility to include redundancy, and power quality. Nevertheless, the topology and control of this converter are relatively complex to design and implement, considering that the converter has a large number of cells and floating capacitors. Therefore multilayer nested control systems are required to maintain the capacitor voltage of each cell regulated within an acceptable range. There are no other review papers where the modelling, control systems and applications of the Modular Multilevel Matrix Converter are discussed. Hence, this paper aims to facilitate further research by presenting the technology related to the Modular Multilevel Matrix Converter, focusing on a comprehensive revision of the modelling and control strategies.