Cellular senescence as the state of permanent inhibition of cell proliferation is a tumour-suppressive mechanism. However, due to the associated secretory phenotype senescence can also contribute to cancer and possibly other age-related diseases, such as obesity, diabetes, atherosclerosis and Alzheimer's disease. There are two major mechanisms of cellular senescence; replicative senescence depends on telomere erosion or dysfunction whilst stress-induced premature senescence (SIPS) is telomere-independent and also includes oncogene-induced senescence (OIS). The senescence phenotype is characterised by altered cellular morphology, increased activity for senescence-associated-β-galactosidase (SA-β-GAL), increased formation of senescence-associated heterochromatin foci (SAHF) and promyelocytic leukemia protein nuclear bodies (PML NBs), permanent DNA damage, chromosomal instability and an inflammatory secretome. Some of these markers have been identified in cells from age-related pathologies. However, to improve our understanding of the contribution of cellular senescence to organismal ageing and age-related disease, it is imperative to define an unequivocal signature of cellular senescence that is functionally connected with normal and pathological ageing. Herein, we describe the processes leading to senescence, and the current biomarkers of cellular senescence, with particular emphasis on the causal role of DNA damage responses involved in the process. We highlight the gaps in our knowledge both of the processes leading to senescence, and the signature of cellular senescence both in vitro and in vivo. A well-defined set of senescence biomarkers for ageing and age-related disease would have a strong impact on the diagnosis, staging and predicted outcomes of age-related disease, providing the basis for a pharmacological intervention to postpone ageing and age-related disease.