Prunus mume Sieb. Et Zucc (P. mume) is an acidic fruit native to China (named Chinese Mei or greengage plum). It is currently cultivated in several Asian countries, including Japan (“Ume”), Korea (Maesil), and Vietnam (Mai or Mo). Due to its myriad nutritional and functional properties, it is accepted in different countries, and its characteristics account for its commercialization. In this review, we summarize the information on the bioactive compounds from the fruit of P. mume and their structure-activity relationships (SAR); the pulp has the highest enrichment of bioactive chemicals. The nutritional properties of P. mume and the numerous uses of its by-products make it a potential functional food. P. mume extracts exhibit antioxidant, anticancer, antimicrobial, and anti-hyperuricaemic properties, cardiovascular protective effects, and hormone regulatory properties in various in vitro and in vivo assays. SAR shows that the water solubility, molecular weight, and chemical conformation of P. mume extracts are closely related to their biological activity. However, further studies are needed to evaluate the fruit’s potential nutritional and functional therapeutic mechanisms. The industrial process of large-scale production of P. mume and its extracts as functional foods or nutraceuticals needs to be further optimized.