Immunotherapy is receiving much attention as a means of treating cancer, but complete, durable responses remain rare for most malignancies. The natural immune system seems to have limitations and deficiencies that might affect its ability to control malignant disease. An alternative to relying on endogenous components in the immune repertoire is to generate lymphocytes with abilities that are greater than those of natural T cells, through genetic modification to produce 'supernatural' T cells. This Review describes how such T cells can circumvent many of the barriers that are inherent in the tumour microenvironment while optimizing T-cell specificity, activation, homing and antitumour function.