Exosomes are small (30–140 nm) lipid bilayer-enclosed particles of endosomal origin. They are a subset of extracellular vesicles (EVs) that are secreted by most cell types. There has been growing interest in exosome research in the last decade due to their emerging role as intercellular messengers and their potential in disease diagnosis. Indeed, exosomes contain proteins, lipids, and RNAs that are specific to their cell origin and could deliver cargo to both nearby and distant cells. As a result, investigation of exosome cargo contents could offer opportunities for disease detection and treatment. Moreover, exosomes have been explored as natural drug delivery vehicles since they can travel safely in extracellular fluids and deliver cargo to destined cells with high specificity and efficiency. Despite significant efforts made in this relatively new field of research, progress has been held back by challenges such as inefficient separation methods, difficulties in characterization, and lack of specific biomarkers. In this review, we summarize the current knowledge in exosome biogenesis, their roles in disease progression, and therapeutic applications and opportunities in bioengineering. Furthermore, we highlight the established and emerging technological developments in exosome isolation and characterization. We aim to consider critical challenges in exosome research and provide directions for future studies.