This paper provides a comprehensive overview of the microgrid (MG) concept, including its definitions, challenges, advantages, components, structures, communication systems, and control methods, focusing on low-bandwidth (LB), wireless (WL), and wired control approaches. Generally, an MG is a small-scale power grid comprising local/common loads, energy storage devices, and distributed energy resources (DERs), operating in both islanded and grid-tied modes. MGs are instrumental to current and future electricity network development, such as a smart grid, as they can offer numerous benefits, such as enhanced network stability and reliability, increased efficiency, an increased integration of clean and renewable energies into the system, enhanced power quality, and so forth, to the increasingly growing and complicated power systems. By considering several objectives in both islanded and grid-tied modes, the development of efficient control systems for different kinds of MGs has been investigated in recent years. Among these control methods, LB communication (LBcom)-based control methods have attracted much attention due to their low expenses, recent developments, and high stability. This paper aims to shed some light on different aspects, a literature review, and research gaps of MGs, especially in the field of their control layers, concentrating on LBcom-based control methods.