Recently, mesenchymal stem/stromal cells (MSCs) and their widespread biomedical applications have attracted great consideration from the scientific community around the world. However, reports have shown that the main populations of the transplanted MSCs are trapped in the liver, spleen, and lung upon administration, highlighting the importance of the development of cell-free therapies. Concerning rising evidence suggesting that the beneficial effects of MSC therapy are closely linked to MSC-released components, predominantly MSC-derived exosomes, the development of an MSC-based cell-free approach is of paramount importance. The exosomes are nano-sized (30–100 nm) lipid bilayer membrane vesicles, which are typically released by MSCs and are found in different body fluids. They include various bioactive molecules, such as messenger RNA (mRNA), microRNAs, proteins, and bioactive lipids, thus showing pronounced therapeutic competence for tissues recovery through the maintenance of their endogenous stem cells, the enhancement of regenerative phenotypic traits, inhibition of apoptosis concomitant with immune modulation, and stimulation of the angiogenesis. Conversely, the specific roles of MSC exosomes in the treatment of various tumors remain challenging. The development and clinical application of novel MSC-based cell-free strategies can be supported by better understanding their mechanisms, classifying the subpopulation of exosomes, enhancing the conditions of cell culture and isolation, and increasing the production of exosomes along with engineering exosomes to deliver drugs and therapeutic molecules to the target sites. In the current review, we deliver a brief overview of MSC-derived exosome biogenesis, composition, and isolation methods and discuss recent investigation regarding the therapeutic potential of MSC exosomes in regenerative medicine accompanied by their double-edged sword role in cancer.