Mesenchymal stem/stromal cells (MSCs) are a reservoir for tissue homeostasis and repair that age during organismal aging. Beside the fundamental in vivo role of MSCs, they have also emerged in the last years as extremely promising therapeutic agents for a wide variety of clinical conditions. MSC use frequently requires in vitro expansion, thus exposing cells to replicative senescence. Aging of MSCs (both in vivo and in vitro) can affect not only their replicative potential, but also their properties, like immunomodulation and secretory profile, thus possibly compromising their therapeutic effect. It is therefore of critical importance to unveil the underlying mechanisms of MSC senescence and to define shared methods to assess MSC aging status. The present review will focus on current scientific knowledge about MSC aging mechanisms, control and effects, including possible anti-aging treatments.