Exosomes, typically 30–150 nm in size, are lipid-bilayered small-membrane vesicles originating in endosomes. Exosome biogenesis is regulated by the coordination of various mechanisms whereby different cargoes (e.g., proteins, nucleic acids, and lipids) are sorted into exosomes. These components endow exosomes with bioregulatory functions related to signal transmission and intercellular communication. Exosomes exhibit substantial potential as drug-delivery nanoplatforms owing to their excellent biocompatibility and low immunogenicity. Proteins, miRNA, siRNA, mRNA, and drugs have been successfully loaded into exosomes, and these exosome-based delivery systems show satisfactory therapeutic effects in different disease models. To enable targeted drug delivery, genetic engineering and chemical modification of the lipid bilayer of exosomes are performed. Stimuli-responsive delivery nanoplatforms designed with appropriate modifications based on various stimuli allow precise control of on-demand drug delivery and can be utilized in clinical treatment. In this review, we summarize the general properties, isolation methods, characterization, biological functions, and the potential role of exosomes in therapeutic delivery systems. Moreover, the effective combination of the intrinsic advantages of exosomes and advanced bioengineering, materials science, and clinical translational technologies are required to accelerate the development of exosome-based delivery nanoplatforms.