Exosomes are endosome-derived nanovesicles involved in cellular communication. They are natural nanocarriers secreted by various cells, making them suitable candidates for diverse drug delivery and therapeutic applications from a material standpoint. They have a phospholipid bilayer decorated with functional molecules and an enclosed parental matrix, which has attracted interest in developing designer/hybrid engineered exosome nanocarriers. The structural versatility of exosomes allows the modification of their original configuration using various methods, including genetic engineering, chemical procedures, physical techniques, and microfluidic technology, to load exosomes with additional cargo for expanded biomedical applications. Exosomes show enormous potential for overcoming the limitations of conventional nanoparticle-based techniques in targeted therapy. This review highlights the exosome sources, characteristics, state of the art in the field of hybrid exosomes, exosome-like nanovesicles and engineered exosomes as potential cargo delivery vehicles for therapeutic applications.