The increasing research and rapid developments in the field of exosomes provide insights into their role and significance in human health. Exosomes derived from various sources, such as mesenchymal stem cells, cardiac cells, and tumor cells, to name a few, can be potential therapeutic agents for the treatment of diseases and could also serve as biomarkers for the early detection of diseases. Cellular components of exosomes, several proteins, lipids, and miRNAs hold promise as novel biomarkers for the detection of various diseases. The structure of exosomes enables them as drug delivery vehicles. Since exosomes exhibit potential therapeutic applications, their efficient isolation from complex biological/clinical samples and precise real-time analysis becomes significant. With the advent of microfluidics, nano-biosensors are being designed to capture exosomes efficiently and rapidly. Herein, we have summarized the history, biogenesis, characteristics, functions, and applications of exosomes, along with the isolation, detection, and quantification techniques. The implications of surface modifications to enhance specificity have been outlined. The review also sheds light on the engineered nanoplatforms being developed for exosome detection and capture.