Power quality (PQ) monitoring and detection has emerged as an essential requirement due to the proliferation of sensitive power electronic interfacing devices, electric vehicle charging stations, energy storage devices, and distributed generation energy sources in the recent smart grid and microgrid scenarios. Even though, to date, the traditional approaches play a vital role in providing a solution to the above issue, the limitations, such as the requirement of significant human effort and not being scalable for large-scale power systems, force us to think of alternative approaches. Looking at a better perspective, deep-learning (DL) has gained the main attraction for various researchers due to its inherent capability to classify the data by extracting dominating and prominent features. This manuscript attempts to provide a comprehensive review of PQ detection and classification based on DL approaches to explore its potential, efficiency, and consistency to produce results accurately. In addition, this state-of-the-art review offers an overview of the novel concepts and the step-by-step method for detecting and classifying PQ events. This review has been presented categorically with DL approaches, such as convolutional neural networks (CNNs), autoencoders, and recurrent neural networks (RNNs), to analyze PQ data. This paper also highlights the challenges and limitations of using DL for PQ analysis, and identifies potential areas for future research. This review concludes that DL algorithms have shown promising PQ detection and classification results, and could replace traditional methods.