Multilevel converters and Matrix converters have been under research and development for more than 3 decades. They are considered today as the state-of-art power conversion systems for high power and power quality demanding application. However this is still a technology under development and many new contributions and new commercial topologies have been reported in the last few years. The use of multilevel matrix converter in renewable, aerospace, vehicle industry can deeply reduce the cost, weight and increase the reliability for the converters. This paper reviews the history of multilevel and matrix converters and discusses the implementation of a new control strategy (Model Predictive Control) for an Indirect and Sparse matrix converter.