The thin red line between the immune system and cancer evolution

•Tumor evolution dynamics are determined by tumor resistant variants selected by intrinsic immune pressure.•The robustness of immune-cell-mediated antitumor response is restricted by high intratumor heterogeneity.•Tumour heterogeneity may offer novel therapeutic opportunities via generation of neo-antigens which can be targeted during immune therapies.•The clonal, as opposed to the subclonal expression of neoantigens, may be mandatory for eliciting robust antitumor responses.•Spatial distribution of neoantigens among different tumor clones hampers the efficient activation of neoantigen-specific T cells.