Exosomes are extracellular vesicles that contain a specific composition of proteins, lipids, RNA, and DNA. They are derived from endocytic membranes and can transfer signals to recipient cells, thus mediating a novel mechanism of cell-to-cell communication. They are also thought to be involved in cellular waste disposal. Exosomes play significant roles in various biological functions, including the transfer of biomolecules such as RNA, proteins, enzymes, and lipids and the regulation of numerous physiological and pathological processes in various diseases. Because of these properties, they are considered to be promising biomarkers for the diagnosis and prognosis of various diseases and may contribute to the development of minimally invasive diagnostics and next generation therapies. The biocompatible nature of exosomes could enhance the stability and efficacy of imaging probes and therapeutics. Due to their potential use in clinical applications, exosomes have attracted much research attention on their roles in health and disease. To explore the use of exosomes in the biomedical arena, it is essential that the basic molecular mechanisms behind the transport and function of these vesicles are well-understood. Herein, we discuss the history, biogenesis, release, isolation, characterization, and biological functions of exosomes, as well as the factors influencing their biogenesis and their technical and biological challenges. We conclude this review with a discussion on the future perspectives of exosomes.