The DNA damage response (DDR) orchestrates DNA repair and halts cell cycle. If damage is not resolved, cells can enter into an irreversible state of proliferative arrest called cellular senescence. Organismal ageing in mammals is associated with accumulation of markers of cellular senescence and DDR persistence at telomeres. Since the vast majority of the cells in mammals are non-proliferating, how do they age? Are telomeres involved? Also oncogene activation causes cellular senescence due to altered DNA replication and DDR activation in particular at the telomeres. Is there a common mechanism shared among apparently distinct types of cellular senescence? And what is the role of telomeric DNA damage?