The objectives of this paper are to review and compare the distributed control methods in AC microgrids and also to identify the impact of communication failure on this type of the controller. The current AC microgrids are distinguished from the traditional power system topologies because of the high penetration of advanced control methods, measurements, sensors, power electronic devices, and communication links. Also, because of the increasing integration of renewable energy sources, control strategy for congestion management, frequency control, and optimal dispatch of microgrids has become more complicated. This paper explains the characteristics and features of distributed control systems and discusses the challenges of these approaches. In addition, a comprehensive review of the advantages and disadvantages of these techniques are explained in detail. On the other hand, the possible challenges, related to communication failure, noise, delay, and packet dropout on the operation of the distributed controller are presented, and several techniques, which reduce the impact of communication failure of the distributed controller, are compared. This comprehensive study on distributed control systems reveals the challenges in and future possible studies on this issue.