This paper surveys the communication networksbased control of cyber-physical microgrids (MGs), including the different architectures of MGs, the control system, and the communication networks within the MGs. The proposed work introduces an overview of the AC, DC, and hybrid AC/DC architectures, highlighting the challenges in the control systems used for each architecture. Focusing on the hierarchical control structure of MGs, we demonstrate the vital role of communication infrastructure in the resilient control of MGs to coordinate between the primary, secondary, and tertiary layers for achieving the control objective. The requirements for communication networks and their influence on MGs' reliable and secure operation are also presented. We have investigated the impact of communication delays, failures, and packet loss on the control system's performance. This survey offers insights into the effects of communication infrastructure on efficient and robust control of cyber-physical MGs in dynamic energy environments.