Knowledge about the mechanisms of action of mesenchymal multipotent stromal cells (MSC) has undergone a significant evolution since their discovery. From the first attempts to use the remarkable properties of MSC in restoring the functions of organs and tissues, the most important question arose – how safe their use would be? One of the aspects of safety of the use of such biomaterial is tumorogenicity and oncogenicity. Numerous studies have shown that the mechanisms by which MSC realize their regenerative potential can, in principle, have a stimulating effect on tumor cells. This review presents specific mechanisms that have a potentially pro-tumor effect, which include the homing of MSC to the tumor site, support for replicative and proliferative signaling of both cancer cells and cancer stem cells, angiogenesis, and effects on the epithelial-mesenchymal transition. Along with pro-tumor mechanisms, the mechanisms of possible antitumor action are also described – direct suppression of tumor growth, loading and transportation of chemotherapeutic agents, oncolytic viruses, genetic modifications for targeting cancer, delivery of “suicide genes” to the tumor. Also, in conclusion, a small review of the current clinical trials of MSC as antitumor agents for malignant neoplasms of various localization (gastrointestinal tract, lungs, ovaries) is given.