Since the 2013 Nobel Prize was awarded for the discovery of vesicle trafficking, a subgroup of nanovesicles called exosomes has been driving the research field to a new regime for understanding cellular communication. This exosome-dominated traffic control system has increased understanding of many diseases, including cancer metastasis, diabetes, and HIV. In addition to the important diagnostic role, exosomes are particularly attractive for drug delivery, due to their distinctive properties in cellular information transfer and uptake. Compared to viral and non-viral synthetic systems, the natural, cell-derived exosomes exhibit intrinsic payload and bioavailability. Most importantly, exosomes easily cross biological barriers, obstacles that continue to challenge other drug delivery nanoparticle systems. Recent emerging studies have shown numerous critical roles of exosomes in many biological barriers, including the blood–brain barrier (BBB), blood–cerebrospinal fluid barrier (BCSFB), blood–lymph barrier (BlyB), blood–air barrier (BAB), stromal barrier (SB), blood–labyrinth barrier (BLaB), blood–retinal barrier (BRB), and placental barrier (PB), which opens exciting new possibilities for using exosomes as the delivery platform. However, the systematic reviews summarizing such discoveries are still limited. This review covers state-of-the-art exosome research on crossing several important biological barriers with a focus on the current, accepted models used to explain the mechanisms of barrier crossing, including tight junctions. The potential to design and engineer exosomes to enhance delivery efficacy, leading to future applications in precision medicine and immunotherapy, is discussed.