In this paper, a multi-input multi-output (MIMO) full-duplex system is addressed, where both the transmitter and receiver have multiple antennas. Fundamental problems of the MIMO full-duplex technique are discussed, and possible solutions are presented. In particular, the transceiver designs that have been reported in the literature are technically reviewed, and their problems are discussed investigating the feasibility of the full-duplex technique in commercialized systems such as LTE and WiFi.