'Cellular senescence', a term originally defining the characteristics of cultured cells that exceed their replicative limit, has been broadened to describe durable states of proliferative arrest induced by disparate stress factors. Proposed relationships between cellular senescence, tumour suppression, loss of tissue regenerative capacity and ageing suffer from lack of uniform definition and consistently applied criteria. Here, we highlight caveats in interpreting the importance of suboptimal senescence-associated biomarkers, expressed either alone or in combination. We advocate that more-specific descriptors be substituted for the now broadly applied umbrella term 'senescence' in defining the suite of diverse physiological responses to cellular stress.