The remarkable success of immune checkpoint inhibitors demonstrates the potential of tumour-specific CD8+ T cells to prevent and treat cancer. Although the number of lives saved by immunotherapy mounts, only a relatively small fraction of patients are cured. Here, we review two of the factors that limit the application of CD8+ T cell immunotherapies: difficulties in identifying tumour-specific peptides presented by MHC class I molecules and the ability of tumour cells to impair antigen presentation as they evolve under T cell selection. We describe recent advances in understanding how peptides are generated from non-canonical translation of defective ribosomal products, relate this to the dysregulated translation that is a feature of carcinogenesis and propose dysregulated translation as an important new source of tumour-specific peptides. We discuss how the synthesis and function of components of the antigen-processing and presentation pathway, including the recently described immunoribosome, are manipulated by tumours for immunoevasion and point to common druggable targets that may enhance immunotherapy.