A microgrid (MG) is a small-scale power system with a cluster of loads and distributed generators operating together through energy management software and devices that act as a single controllable entity with respect to the grid. MG has become a key research element in smart grid and distribution power systems. MG mainly contains different renewable energy sources (RESs) that use various technological advancements, such as power electronics-based technologies. However, it has an unstable output, thereby causing different types of power quality (PQ) events. As a result, standards and mitigation methods have been developed in recent years. To mitigate PQ issues due to MG integration, various methods and standards have been proposed over the last years. Although these individual methods are well documented, a comparative overview had not been introduced so far. Thus, this study aims to fill the gap by reviewing and comparing the prior-art PQ issues, solutions, and standards in MGs. We compare the main issues related to voltage sag, voltage swell, voltage and current harmonics, system unbalances, and fluctuations to ensure high-quality MG output power. The new technologies associated with MGs generate harmonics emission in the range of 2–150 kHz, thereby causing a new phenomenon, namely, supraharmonics (SH) emission, which is not sufficiently covered in the literature. Therefore, the characteristics, causes, consequences, and measurements of SH are highlighted and analyzed. The mitigation strategies, control, and devices of PQ issues are also discussed. Moreover, a comparison is conducted between the most popular devices used to mitigate the PQ issues in MG in terms of cost, rating, and different aspects of performance. This review study can strengthen the efforts toward the mitigation and standards development of PQ issues in MG applications, especially SH. Finally, some recommendations and suggestions to improve PQ of MG, including SH, are highlighted.