The issue of power quality (PQ) has become more prominent over the last few decades as the demand of clean and high quality power is increasing around the globe. The effect of power quality disturbances on the equipment most of the time is very destructive, usually generates disruptions, which consecutively affects the other load connected to the power systems. The main purpose of this article is to present a comprehensive review of various power quality analysis techniques such as heuristic optimization, signal processing, machine learning, neural networks, artificial intelligence, and hardware implementation, so that a brief overview will be presented to the researcher and power engineers working in the field of power quality. Additionally, a comparative analysis is also reported on various methods based on several criteria including timing and accuracy, use of industrial and non-industrial data set, noisy and noiseless conditions, and finally single and multiple power quality events for analysis. More than 200 research publications are included for analysis and listed in reference so that it will be easy for the researcher in the domain of power quality to explore the possibility of further improvement in this field.