Neurodegenerative diseases constitute a group of pathologies whose etiology remains unknown in many cases, and there are no treatments that stop the progression of such diseases. Moreover, the existence of the blood–brain barrier is an impediment to the penetration of exogenous molecules, including those found in many drugs. Exosomes are extracellular vesicles secreted by a wide variety of cells, and their primary functions include intercellular communication, immune responses, human reproduction, and synaptic plasticity. Due to their natural origin and molecular similarities with most cell types, exosomes have emerged as promising therapeutic tools for numerous diseases. Specifically, neurodegenerative diseases have shown to be a potential target for this nanomedicine strategy due to the difficult access to the brain and the strategy’s pathophysiological complexity. In this regard, this review explores the most important biological-origin drug delivery systems, innovative isolation methods of exosomes, their physicochemical characterization, drug loading, cutting-edge functionalization strategies to target them within the brain, the latest research studies in neurodegenerative diseases, and the future challenges of exosomes as nanomedicine-based therapeutic tools.