This paper offers a systematic literature review of real-time detection and classification of Power Quality Disturbances (PQDs). A particular focus is given to voltage sags and notches, as voltage sags cause huge economic losses while research on voltage notches is still very incipient. A systematic method based on scientometrics, text similarity and the analytic hierarchy process is proposed to structure the review and select the most relevant literature. A bibliometric analysis is then performed on the bibliographic data of the literature to identify relevant statistics such as the evolution of publications over time, top publishing countries, and the distribution by relevant topics. A set of articles is subsequently selected to be critically analyzed. The critical review is structured in steps for real-time detection and classification of PQDs, namely, input data preparation, preprocessing, transformation, feature extraction, feature selection, detection, classification, and characterization. Aspects associated with the type of disturbance(s) addressed in the literature are also explored throughout the review, including the perspectives of those studies aimed at multiple PQDs, or specifically focused on voltage sags or voltage notches. The real-time performance of the reviewed tools is also examined. Finally, unsolved issues are discussed, and prospects are highlighted.