Exosomes are tiny vesicles with a double membrane structure that cells produce. They range in diameter from 40 to 150 nm and may contain a variety of biomolecules including proteins and nucleic acids. Exosomes have low toxicity, low immunogenicity, and the ability to encapsulate a wide variety of substances, making them attractive drug delivery vehicles. MSCs secrete large amounts of exosomes and hence serve as an excellent source of exosomes. MSCs-derived exosomes have regenerative and tissue repair functions comparable to MSCs and can circumvent the risks of immune rejection and infection associated with MSC transplantation, indicating that they may be a viable alternative to MSCs’ biological functions. In this review, we summarized the drug delivery methods and advantages of exosomes, as well as the advancement of MSC exosomes as drug carriers. The challenges and prospects of using exosomes as drug delivery vectors are presented.