The term “exosomes” is currently used to describe specific vesicular structures of endosomal origin produced by the majority of eukaryotic cells. These natural vesicles have been under study for more than two decades. Nevertheless, a real splash of scientific interest in studies on exosomes took place only during recent years, when the concept of the role and functions of exosomes in multicellular organisms was essentially reconsidered. The major role in this was played by the discovery of exosomal mRNA and miRNA in 2007, which stimulated the idea of regulatory and communicative role of exosomes in the organism and also encouraged considering exosomes and other vesicles as potential biomarkers. The present review summarizes the up to date knowledge on the composition and probable physiological functions of nucleic acids released by different cells as components of exosomes. We also touch upon the problem of using these data in clinical diagnosis.