In recent years, the adoption of statistical process monitoring (SPM) techniques in healthcare has been successful. For instance, biosurveillance and biosignal monitoring have demonstrated direct benefits. As the latest reviews of the literature show, parametric SPM techniques have been implemented to evaluate the quality-of-service hospitals provide, track medical equipment, monitor safety markers, or assess the improvements made by quality projects. However, as shown in this research, world-trending topics in data science that include data-driven approaches integrated with SPM have not been reviewed. To bridge this gap and shed light on new research, a systematic review of scientific databases and a taxonomic literature analysis were performed. For the scientometric analysis, a set of bibliometric indicators were obtained to portray the performance of each subtopic, such as examining growth kinetics, identifying top authors, journals, countries and affiliations, as well as creating network maps of co-authorship and keyword co-occurrence. Additionally, the taxonomic analysis involved grouping proposals by methodological approach. Each approach was explained and discussed to identify the advantages, limitations, and challenges that researchers and practitioners may encounter. SPM researchers and practitioners require more flexibility in data-driven approaches to account for frequency unbalance, complexity, dimensionality problems, and speed. Those working in data-driven and computer-oriented areas can expand their toolbox by incorporating sequential approaches to enhance the power of their classifiers, assess risk, reduce misspecification, and adopt model-oriented mindsets.