Immune checkpoints arise from physiological changes during tumorigenesis that reprogramme inflammatory, immunological and metabolic processes in malignant lesions and local lymphoid tissues, which constitute the immunological tumour microenvironment (TME). Improving clinical responses to immune checkpoint blockade will require deeper understanding of factors that impact local immune balance in the TME. Elevated catabolism of the amino acids tryptophan (Trp) and arginine (Arg) is a common TME hallmark at clinical presentation of cancer. Cells catabolizing Trp and Arg suppress effector T cells and stabilize regulatory T cells to suppress immunity in chronic inflammatory diseases of clinical importance, including cancers. Processes that induce Trp and Arg catabolism in the TME remain incompletely defined. Indoleamine 2,3 dioxygenase (IDO) and arginase 1 (ARG1), which catabolize Trp and Arg, respectively, respond to inflammatory cues including interferons and transforming growth factor-β (TGFβ) cytokines. Dying cells generate inflammatory signals including DNA, which is sensed to stimulate the production of type I interferons via the stimulator of interferon genes (STING) adaptor. Thus, dying cells help establish local conditions that suppress antitumour immunity to promote tumorigenesis. Here, we review evidence that Trp and Arg catabolism contributes to inflammatory processes that promote tumorigenesis, impede immune responses to therapy and might promote neurological comorbidities associated with cancer.