The essence of enzymes is to keep the homeostasis and balance of humans by catalyzing metabolic responses and modulating cells. Suppression of an enzyme slows the progress of some diseases, making it a therapeutic target. Therefore, it is important to develop enzyme inhibitors by proper bioactivity screening strategies for the future treatment of some major diseases. In this review, we summarized the recent (2015–2020) applications of several screening strategies (electrophoretically mediated microanalysis, enzyme immobilization, affinity chromatography, and affinity ultrafiltration) in finding enzyme inhibitors from certain species of bioactive natural compounds of plant origin (flavonoids, alkaloids, phenolic acids, saponins, anthraquinones, coumarins). At the same time, the advantages and disadvantages of each strategy were also discussed, and the future possible development direction in enzyme inhibitor screening has been prospected. To sum up, it is expected to help readers select suitable screening strategies for enzyme inhibitors and provide useful information for the study of the biological effects of specific kinds of natural products.