Mesenchymal stem cells (MSCs) hold great promise for the treatment of numerous diseases. A major problem for MSC therapeutic use is represented by the very low amount of MSCs which can be isolated from different tissues; thus ex vivo expansion is indispensable. Long-term culture, however, is associated with extensive morphological and functional changes of MSCs. In addition, the concern that they may accumulate stochastic mutations which lead the risk of malignant transformation still remains. Overall, the genome of human MSCs (hMSCs) appears to be apparently stable throughout culture, though transient clonal aneuploidies have been detected. Particular attention should be given to the use of low-oxygen environment in order to increase the proliferative capacity of hMSCs, since data on the effect of hypoxic culture conditions on genomic stability are few and contradictory. Furthermore, specific and reproducible epigenetic changes were acquired by hMSCs during ex vivo expansion, which may be connected and trigger all the biological changes observed. In this review we address current issues on long-term culture of hMSCs with a 360-degree view, starting from the genomic profiles and back, looking for an epigenetic interpretation of their genetic stability.