Power quality is the manifestation of a disruption in the supply voltage, current or frequency that damages the utility equipment and has become an important issue with the introduction of more sophisticated and sensitive devices. So, the supply power quality issue still remains a major challenge as its degradation can cause huge destabilization of electrical networks. As renewable energy sources have irregular nature, a microgrid essentially needs energy storage system containing advanced power electronic converters which is the root cause of majority of power quality disturbances. Also, the integration of non-linear and unbalanced loads into the grid adds to its power quality problems. This article gives a compact overview on the identification, categorization and mitigation of these power quality events in a microgrid by using various Artificial Intelligence-based techniques like Optimization techniques, Adaptive Learning techniques, Signal Processing and Pattern Recognition, Neural Networks and Fuzzy Logic.