CD8+ T cells specific for cancer cells are detected within tumours. However, despite their presence, tumours progress. The clinical success of immune checkpoint blockade and adoptive T cell therapy demonstrates the potential of CD8+ T cells to mediate antitumour responses; however, most patients with cancer fail to achieve long-term responses to immunotherapy. Here we review CD8+ T cell differentiation to dysfunctional states during tumorigenesis. We highlight similarities and differences between T cell dysfunction and other hyporesponsive T cell states and discuss the spatio-temporal factors contributing to T cell state heterogeneity in tumours. An important challenge is predicting which patients will respond to immunotherapeutic interventions and understanding which T cell subsets mediate the clinical response. We explore our current understanding of what determines T cell responsiveness and resistance to immunotherapy and point out the outstanding research questions.