Although evidence shows that anthocyanins present promising health benefits, their poor stability still limits their applications in the food industry. Increasing the stability of anthocyanins is necessary to promote their absorption and metabolism and improve their health benefits. Numerous encapsulation approaches have been developed for the targeted release of anthocyanins to retain their bioactivities and ameliorate their unsatisfactory stability. Generally, choosing suitable edible encapsulation materials based on biopolymers is important in achieving the expected goals. This paper presented an ambitious task of summarizing the current understanding and challenges of biopolymer-based anthocyanin encapsulation in detail. The food-grade edible microencapsulation materials, especially for proteins and polysaccharides, should be employed to improve the stability of anthocyanins for effective application in the food industry. The influence factors involved in anthocyanin stability were systematically reviewed and highlighted. Food-grade proteins, especially whey protein, caseinate, gelatin, and soy protein, are attractive in the food industry for encapsulation owing to the improvement of stability and their health benefits. Polysaccharides, such as starch, pectin, chitosan, cellulose, mucilages, and their derivatives, are used as encapsulation materials because of their satisfactory biocompatibility and biodegradability. Moreover, the challenges and perspectives for the application of anthocyanins in food products were presented based on current knowledge. The proposed perspective can provide new insights into the amelioration of anthocyanin bioavailability by edible biopolymer encapsulation.