Matrix converters (MCs) allow the implementation of single-stage AC/AC power conversion systems (PCS) with inherent bidirectional power flow capability. By avoiding the typical DC-link capacitor, MCs have the potential to achieve higher power density with a more reliable operation and less maintenance when compared with conventional two-stage AC/DC/AC PCS. For these reasons, matrix converters have been receiving significant attention from the academic sector but have not yet been implemented on a large industrial scale. This article reviews the Direct Matrix Converter (DMC) and the Indirect Matrix Converter (IMC) along with the respective actual and most important modulation methods. Simulation results are provided to validate the theoretical analysis and to get a deep insight about the implementation of space vector modulation (SVM) and respective switching pattern generator.