Exosomes are a type of extracellular vesicles, produced within multivesicular bodies, that are then released into the extracellular space through a merging of the multivesicular body with the plasma membrane. These vesicles are secreted by almost all cell types to aid in a vast array of cellular functions, including intercellular communication, cell differentiation and proliferation, angiogenesis, stress response, and immune signaling. This ability to contribute to several distinct processes is due to the complexity of exosomes, as they carry a multitude of signaling moieties, including proteins, lipids, cell surface receptors, enzymes, cytokines, transcription factors, and nucleic acids. The favorable biological properties of exosomes including biocompatibility, stability, low toxicity, and proficient exchange of molecular cargos make exosomes prime candidates for tissue engineering and regenerative medicine. Exploring the functions and molecular payloads of exosomes can facilitate tissue regeneration therapies and provide mechanistic insight into paracrine modulation of cellular activities. In this review, we summarize the current knowledge of exosome biogenesis, composition, and isolation methods. We also discuss emerging healing properties of exosomes and exosomal cargos, such as microRNAs, in brain injuries, cardiovascular disease, and COVID-19 amongst others. Overall, this review highlights the burgeoning roles and potential applications of exosomes in regenerative medicine.