Exosomes are cell-derived, nano-sized extracellular vesicles comprising a lipid bilayer membrane that encapsulates several biological components, such as nucleic acids, lipids, and proteins. The role of exosomes in cell–cell communication and cargo transport has made them promising candidates in drug delivery for an array of diseases. Despite several research and review papers describing the salient features of exosomes as nanocarriers for drug delivery, there are no FDA-approved commercial therapeutics based on exosomes. Several fundamental challenges, such as the large-scale production and reproducibility of batches, have hindered the bench-to-bedside translation of exosomes. In fact, compatibility and poor drug loading sabotage the possibility of delivering several drug molecules. This review provides an overview of the challenges and summarizes the potential solutions/approaches to facilitate the clinical development of exosomal nanocarriers.