Extracellular vesicles (EVs) such as ectosomes and exosomes have gained attention as promising natural carriers for drug delivery. Exosomes, which range from 30 to 100 nm in diameter, possess a lipid bilayer and are secreted by various cells. Due to their high biocompatibility, stability, and low immunogenicity, exosomes are favored as cargo carriers. The lipid bilayer membrane of exosomes also offers protection against cargo degradation, making them a desirable candidate for drug delivery. However, loading cargo into exosomes remains to be a challenge. Despite various strategies such as incubation, electroporation, sonication, extrusion, freeze–thaw cycling, and transfection that have been developed to facilitate cargo loading, inadequate efficiency still persists. This review offers an overview of current cargo delivery strategies using exosomes and summarizes recent approaches for loading small-molecule, nucleic acid, and protein drugs into exosomes. With insights from these studies, we provide ideas for more efficient and effective delivery of drug molecules by using exosomes.