Despite the tremendous efforts of many researchers and clinicians, cancer remains the second leading cause of mortality worldwide. Mesenchymal stem/stromal cells (MSCs) are multipotent cells residing in numerous human tissues and presenting unique biological properties, such as low immunogenicity, powerful immunomodulatory and immunosuppressive capabilities, and, in particular, homing abilities. Therapeutic functions of MSCs are mediated mostly by the paracrine effect of released functional molecules and other variable components, and among them the MSC-derived extracellular vesicles (MSC-EVs) seem to be one of the central mediators of the therapeutic functions of MSCs. MSC-EVs are membrane structures secreted by the MSCs, rich in specific proteins, lipids, and nucleic acids. Amongst these, microRNAs have achieved the most attention currently. Unmodified MSC-EVs can promote or inhibit tumor growth, while modified MSC-EVs are involved in the suppression of cancer progression via the delivery of therapeutic molecules, including miRNAs, specific siRNAs, or suicide RNAs, as well as chemotherapeutic drugs. Here, we present an overview of the characteristics of the MSCs-EVs and describe the current methods for their isolation and analysis, the content of their cargo, and modalities for the modification of MSC-EVs in order for them to be used as drug delivery vehicles. Finally, we describe different roles of MSC-EVs in the tumor microenvironment and summarize current advances of MCS-EVs in cancer research and therapy. MSC-EVs are expected to be a novel and promising cell-free therapeutic drug delivery vehicle for the treatment of cancer.