The micro- and nanoencapsulation of bioactive compounds has resulted in a large improvement in the food, nutraceutical, pharmaceutical, and agriculture industries. These technologies serve, on one side, to protect, among others, vitamins, minerals, essential fatty acids, polyphenols, flavours, antimicrobials, colorants, and antioxidants, and, on the other hand, to control the release and assure the delivery of the bioactive compounds, targeting them to specific cells, tissues, or organs in the human body by improving their absorption/penetration through the gastrointestinal tract. The food industry has been applying nanotechnology in several ways to improve food texture, flavour, taste, nutrient bioavailability, and shelf life using nanostructures. The use of micro- and nanocapsules in food is an actual trend used mainly in the cereal, bakery, dairy, and beverage industries, as well as packaging and coating. The elaboration of bio capsules with high-value compounds from agro-industrial by-products is sustainable for the natural ecosystem and economically interesting from a circular economy perspective. This critical review presents the principal methodologies for performing micro- and nanoencapsulation, classifies them (top-down and/or bottom-up), and discusses the differences and advantages among them; the principal types of encapsulation systems; the natural plant sources, including agro-industrial by-products, of bioactive compounds with interest for the food industry to be encapsulated; the bioavailability of encapsulates; and the main techniques used to analyse micro- and nanocapsules. Research work on the use of encapsulated bioactive compounds, such as lycopene, hydroxytyrosol, and resveratrol, from agro-industrial by-products must be further reinforced, and it plays an important role, as it presents a high potential for the use of their antioxidant and/or antimicrobial activities in food applications and, therefore, in the food industry. The incorporation of these bioactive compounds in food is a challenge and must be evaluated, not only for their nutritional aspect, but also for the chemical safety of the ingredients. The potential use of these products is an available economical alternative towards a circular economy and, as a consequence, sustainability.