Extra virgin olive oil is characterized by its high content of unsaturated fatty acid residues in triglycerides, mainly oleic acid, and the presence of bioactive and antioxidant compounds. Its consumption is associated with lower risk of suffering chronic diseases and unwanted processes linked to aging, due to the antioxidant capacity and capability of its components to modulate cellular signaling pathways. Consumption of olive oil can alter the physiology of mesenchymal stem cells (MSCs). This may explain part of the healthy effects of olive oil consumption, such as prevention of unwanted aging processes. To date, there are no specific studies on the action of olive oil on MSCs, but effects of many components of such food on cell viability and differentiation have been evaluated. The objective of this article is to review existing literature on how different compounds of extra virgin olive oil, including residues of fatty acids, vitamins, squalene, triterpenes, pigments and phenols, affect MSC maintenance and differentiation, in order to provide a better understanding of the healthy effects of this food. Interestingly, most studies have shown a positive effect of these compounds on MSCs. The collective findings support the hypothesis that at least part of the beneficial effects of extra virgin olive oil consumption on health may be mediated by its effects on MSCs.