Exosomes as nanosized vesicles are emerging as drug delivery systems for therapeutics owing to their natural origin, their ability to mediate intercellular communication, and their potential to encapsulate various biological molecules such as proteins and nucleic acids within the lipid bilayer membrane or in the lumen. Exosomes contain endogenous components (proteins, lipids, RNA) that could be used to deliver cargoes to target cells, offering an opportunity to diagnose and treat various diseases. Owing to their ability to travel safely in extracellular fluid and to transport cargoes to target cells with high efficacy, exosomes offer enhanced delivery of cargoes in vivo. However, several challenges related to the stabilization of the exosomes, the production of sufficient amounts of exosomes with safety and efficacy, the efficient loading of drugs into exosomes, the clearance of exosomes from circulation, and the transition from the bench scale to clinical production may limit their development and clinical use. For the clinical use of exosomes, it is important to understand the molecular mechanisms behind the transport and function of exosome vesicles. This review exploits techniques related to the isolation and characterization of exosomes and their drug delivery potential to enhance the therapeutic outcome and stabilization methods. Further, routes of administration, clinical trials, and regulatory aspects of exosomes will be discussed in this review.