Exosomes are nanovesicles 40–120 nm in diameter secreted by almost all cell types and providing humoral intercellular interactions. Given the natural origin and high biocompatibility, the potential for loading various anticancer molecules and therapeutic nucleic acids inside, and the surface modification possibility for targeted delivery, exosomes are considered to be a promising means of delivery to cell cultures and experimental animal organisms. Milk is a unique natural source of exosomes available in semi-preparative and preparative quantities. Milk exosomes are highly resistant to the harsh conditions of the gastrointestinal tract. In vitro studies have demonstrated that milk exosomes have an affinity to epithelial cells, are digested by cells by endocytosis mechanism, and can be used for oral delivery. With milk exosome membranes containing hydrophilic and hydrophobic components, exosomes can be loaded with hydrophilic and lipophilic drugs. This review covers a number of scalable protocols for isolating and purifying exosomes from human, cow, and horse milk. Additionally, it considers passive and active methods for drug loading into exosomes, as well as methods for modifying and functionalizing the surface of milk exosomes with specific molecules for more efficient and specific delivery to target cells. In addition, the review considers various approaches to visualize exosomes and determine cellular localization and bio-distribution of loaded drug molecules in tissues. In conclusion, we outline new challenges for studying milk exosomes, a new generation of targeted delivery agents.