Adult human mesenchymal stem cells (hMSCs) can differentiate into several cell lineages – consequently, they have promise as therapies in regenerative medicine. When grown in culture, however, hMSCs rapidly undergo senescence, which could impact on their use as therapeutic agents. Nuclear structural alteration is a key feature of senescence in many cell types; now, Vered Raz and colleagues (p. 4018) use newly developed quantitative image-processing tools to analyse how the nuclear architecture of hMSCs changes during senescence. The authors show that, early in senescence, the nuclear lamina of hMSCs becomes deformed and gives rise to intranuclear structures; in addition, centromeres and telomeres of chromosomes relocalise to a peripheral nuclear position that spatially overlaps with these structures. The authors observe that, during senescence, telomeres form large aggregates that colocalise with the DNA-damage marker γ-H2AX but not with the telomerase component TERT. Notably, the binding of telomere aggregates to lamina structures is enhanced when the lamina is distorted through the expression of mutant lamins. Thus, the nuclear lamina of senescent hMSCs regulates the spatial positioning of heterochromatic chromosome regions. These data shed light on how nuclear architecture changes during hMSC senescence.