‘T cell exhaustion’ is a broad term that has been used to describe the response of T cells to chronic antigen stimulation, first in the setting of chronic viral infection but more recently in response to tumours. Understanding the features of and pathways to exhaustion has crucial implications for the success of checkpoint blockade and adoptive T cell transfer therapies. In this Viewpoint article, 18 experts in the field tell us what exhaustion means to them, ranging from complete lack of effector function to altered functionality to prevent immunopathology, with potential differences between cancer and chronic infection. Their responses highlight the dichotomy between terminally differentiated exhausted T cells that are TCF1^– and the self-renewing TCF1⁺ population from which they derive. These TCF1⁺ cells are considered by some to have stem cell-like properties akin to memory T cell populations, but the developmental relationships are unclear at present. Recent studies have also highlighted an important role for the transcriptional regulator TOX in driving the epigenetic enforcement of exhaustion, but key questions remain about the potential to reverse the epigenetic programme of exhaustion and how this might affect the persistence of T cell populations.