Cellular immunotherapy is now the focus of huge attention and investment from the biopharmaceutical industry, with many early-phase trials demonstrating impressive clinical responses. Spatial-omics demonstrate some causes of poor immunotherapy response, such as infiltration of only exhausted T cells into the tumour niche during checkpoint blockade therapy, or endogenous cytotoxic T cells and/or chimeric antigen receptor (CAR)-T cells remaining excluded from the tumour by physical barriers, such as trapping by stroma. Tumour antigens can be therapeutically targeted by vaccination or by adoptive transfer of antigen-specific T cells. A more pharmacological ‘off-the-shelf’ approach to engage native T cells against malignant cells is by using bispecific T-cell engagers and bispecific antibodies. Early trials of natural killer (NK)-cell immunotherapy were based upon infusion of autologous NK cell-activating cytokines or ex vivo activated NK cells, but were largely disappointing.