Nanomedicine aims to exploit the improved and often novel physical, chemical, and biological properties of materials at the nanometric scale, possibly with the highest level of biomimetism, an approach that simulates what occurs in nature. Although extracellularly released vesicles include both microvesicles (MVs) and exosomes, only exosomes have the size that may be considered suitable for potential use in nanomedicine. In fact, recent reports have shown that exosomes are able to interact with target cells within an organ or at a distance using different mechanisms. Much is yet to be understood about exosomes, and currently, we are looking at the visible top of an iceberg, with most of what we have to understand on these nanovesicles still under the sea. In fact, we know that exosomes released by normal cells always trigger positive effects, whereas those released by cells in pathological condition, such as tumor or infected cells, may induce undesired, dangerous, and mostly unknown effects, but we cannot exclude the possibility that exosomes may also be detrimental for the body in normal conditions. However, whether we consider extracellular vesicles as a whole, thus including MVs, it appears that even in normal conditions, extracellular vesicles may lead to unwanted effects, depending on gender and age. This review aims to critically emphasize existing data in the literature that support the possible roles of exosomes in both diagnostic and therapeutic scopes.