Ageing is a complex biological process in which a gradual decline in physiological fitness increases susceptibility to diseases such as neurodegenerative disorders and cancer. Cellular senescence, a state of irreversible cell-growth arrest accompanied by functional deterioration, has emerged as a pivotal driver of ageing. In this Review, we discuss how heterochromatin loss, telomere attrition and DNA damage contribute to cellular senescence, ageing and age-related diseases by eliciting genome instability, innate immunity and inflammation. We also discuss how emerging therapeutic strategies could restore heterochromatin stability, maintain telomere integrity and boost the DNA repair capacity, and thus counteract cellular senescence and ageing-associated pathologies. Finally, we outline current research challenges and future directions aimed at better comprehending and delaying ageing.