This article presents a review and a comparison of the conventional matrix converter (CMC), multimodular matrix converter (MMMC), and multilevel matrix modular converter (M3C) topologies, which are three of the main topologies of the matrix family. The study of the CMC supplies basic knowledge for these structures and then the concept of multilevel matrix converters used in MMMC and M3C topologies is approached. The study addresses modulation strategies and switching sequences for the topologies to provide implementation guidelines and harmonic content reduction. The design is also carried out and results of the three topologies are shown to exemplify their operation. Finally, the article presents a comparison between the topologies to highlight the advantages and challenges of each one. This study contributes information on the three topologies, which are not easily found in the literature, especially in terms of modulation and switching strategies. It also highlights applications and research points that have to improve.