In this Timeline, we describe the characteristics of tumour antigens that are recognized by spontaneous T cell responses in cancer patients and the paths that led to their identification. We explain on what genetic basis most, but not all, of these antigens are tumour specific: that is, present on tumour cells but not on normal cells. We also discuss how strategies that target these tumour-specific antigens can lead either to tumour-specific or to crossreactive T cell responses, which is an issue that has important safety implications in immunotherapy. These safety issues are even more of a concern for strategies targeting antigens that are not known to induce spontaneous T cell responses in patients.