Microgrids (MG) are small-scale electric grids with local voltage control and power management systems to facilitate the high penetration and grid integration of renewable energy resources (RES). The distributed generation units (DGs), including RESs, are connected to (micro) grids through power electronics-based inverters. Therefore, new paradigms are required for voltage and frequency regulation by inverter-interfaced DGs (IIDGs). Notably, employing effective voltage and frequency regulation methods for establishing power-sharing among parallel inverters in MGs is the most critical issue. This paper provides a comprehensive study, comparison, and classification of control methods including communication-based, decentralized, and construction and compensation control techniques. The development of inverter-dominated MGs has caused limitations in employing classical control techniques due to their defective performance in handling non-linear models of IIDGs. To this end, this article reviews and illustrates advanced controllers that can deal with the challenges that are created due to the uncertain and arbitrary impedance characteristics of IIDGs in dynamics/transients.