Exosomes are becoming increasingly important therapeutic biomaterials for use in a variety of therapeutic applications due to their unique characteristics, especially due to the ineffectiveness and cytotoxicity of some existing therapies and synthetic therapeutic nanocarriers. They are highly promising as carriers of drugs, genes, and other therapeutic agents that can be incorporated into their interior or onto their surface through various modification techniques to improve their targeting abilities. In addition, they are biocompatible, safe, and stable. The review focuses on different types of exosomes and methods of their preparation, including the incorporation of different kinds of cargo, especially for drug delivery purposes. In particular, their importance and effectiveness as delivery vehicles of various therapeutic agents for a variety of therapeutic applications, including different diseases and disorders such as cancer treatment, cardiovascular and neurodegenerative diseases, are emphasized. Administration routes of exosomes into the body are also included. A novelty in the article is the emphasis on global companies that are already successfully developing and testing such therapeutic biomaterials, with a focus on the most influential ones. Moreover, a comparison of the advantages and disadvantages of the various methods of exosome production is summarized for the first time.