Somatic mutations in cancer cells can generate tumour-specific neoepitopes, which are recognized by autologous T cells in the host. As neoepitopes are not subject to central immune tolerance and are not expressed in healthy tissues, they are attractive targets for therapeutic cancer vaccines. Because the vast majority of cancer mutations are unique to the individual patient, harnessing the full potential of this rich source of targets requires individualized treatment approaches. Many computational algorithms and machine-learning tools have been developed to identify mutations in sequence data, to prioritize those that are more likely to be recognized by T cells and to design tailored vaccines for every patient. In this Review, we fill the gaps between the understanding of basic mechanisms of T cell recognition of neoantigens and the computational approaches for discovery of somatic mutations and neoantigen prediction for cancer immunotherapy. We present a new classification of neoantigens, distinguishing between guarding, restrained and ignored neoantigens, based on how they confer proficient antitumour immunity in a given clinical context. Such context-based differentiation will contribute to a framework that connects neoantigen biology to the clinical setting and medical peculiarities of cancer, and will enable future neoantigen-based therapies to provide greater clinical benefit.