Telomere shortening induces cellular senescence in proliferative cells. Yet, it is presently unclear how it is triggered in post‐mitotic cells such as cardiac myocytes. A new study by Anderson et al (2019) reports that during ageing of the heart, cellular senescence develops independently of telomere length, but is evoked by DNA damage, which preferentially accumulates at the telomere. Removal of senescent cells using senolytic drugs ameliorated cardiac hypertrophy and fibrosis and may inform novel approaches to improve the conditions for the ageing heart.