Progress in Microgrid (MG) research has evolved the MG concept from classical, purely MG power networks to more advanced power and communications networks. The communications infrastructure helps control and manage the unreliable power outputs that most standard power generation elements of the MG (e.g., wind turbines and photo-voltaic panels) deliver. Although communication technologies do offer certain advantages for sensing and control, they generate other complications due to packet loss and packet latency, among other transmission impairments. In this work, we discuss the impact of communications on MG performance, establishing the requirements of data exchanges and system response in the three levels of a hierarchical control approach: primary, secondary, and tertiary. With a focus on the secondary level-responsible for ensuring the restoration of electrical parameters-we identify standards, networking protocols, and communication technologies relevant for the interoperability of MGs and clusters of MGs, including both modes of operation: isolated and grid-connected. We review theoretical approaches and practical implementations that consider the effects of the communications network on the general performance of the MG. Moreover, we undertake an experimental analysis of the influence of wired and wireless communication networks on MG performance, revealing the importance of designing future smart control solutions more robust to communication degradation, especially if wireless technologies are integrated to provide scalable deployments. Aspects such as resilience, security, and interoperability are also shown to require continuing efforts in research and practical applications.