Intercellular communications play a major role in tissue homeostasis and responses to external cues. Novel structures for this communication have recently been described. These tunneling nanotubes (TNTs) consist of thin-extended membrane protrusions that connect cells together. TNTs allow the cell-to-cell transfer of various cellular components, including proteins, RNAs, viruses, and organelles, such as mitochondria. Mesenchymal stem cells (MSCs) are both naturally present and recruited to many different tissues where their interaction with resident cells via secreted factors has been largely documented. Their immunosuppressive and repairing capacities constitute the basis for many current clinical trials. MSCs recruited to the tumor microenvironment also play an important role in tumor progression and resistance to therapy. MSCs are now the focus of intense scrutiny due to their capacity to form TNTs and transfer mitochondria to target cells, either in normal physiological or in pathological conditions, leading to changes in cell energy metabolism and functions, as described in this review.