This paper presents an analysis of a new application of different direct matrix converter topologies used as power interfaces in AC, DC, and hybrid microgrids, with model predictive current control. Such a combination of a converter and control strategy leads to a high power quality microgrid voltage, even with a low power quality main grid voltage and even during the connection and disconnection of a variety of loads and generation sources to the microgrids. These robust systems are suitable for applications in which sensitive loads are to be supplied and these loads are connected close to distributed-generation sources with inherent intermittent behavior. The authors also propose the use of new direct matrix converter configurations with a reduced number of switches in order to achieve reduced cost, reduced failure rate, and higher reliability, which are very desirable in microgrids. Finally, the authors also introduce new hybrid direct matrix converter topologies that provide interesting options for the islanded operation of the microgrids with the use of a battery system. In other words, the proposed hybrid direct matrix converters result in flexible hybrid microgrid configurations integrating DC and AC devices with high power quality and high power supply reliability.