Mesenchymal stem/stromal cells (MSCs) are involved in the maintenance and regeneration of a large variety of tissues due to their stemness and multi-lineage differentiation capability. Harnessing these advantageous features, a flurry of clinical trials have focused on MSCs to treat different pathologies, but only few protocols have received regulatory approval so far. Among the various causes hindering MSCs’ efficacy is the emergence of cellular senescence, which has been correlated with specific characteristics, such as morphological and epigenetic alterations, DNA damage, ROS production, mitochondrial dysfunction, telomere shortening, non-coding RNAs, loss of proteostasis, and a peculiar senescence-associated secretory phenotype. Several strategies have been investigated for delaying or even hopefully reverting the onset of senescence, as assessed by the senescent phenotype of MSCs. Here, the authors reviewed the most updated literature on the potential causes of senescence, with a particular emphasis on the current and future therapeutic approaches aimed at reverting senescence and/or extending the functional lifespan of stem cells.