Chimeric antigen receptor (CAR) therapy is based on patient blood-derived T cells and natural killer cells, which are engineered in vitro to recognize a target antigen in cancer cells. Most CAR-T recognize target antigens through immunoglobulin antigen-binding regions. Hence, CAR-T cells do not require the major histocompatibility complex presentation of a target peptide. CAR-T therapy has been tremendously successful in the treatment of leukemias. On the other hand, the clinical efficacy of CAR-T cells is rarely detected against solid tumors. CAR-T-cell therapy of cancer faces many hurdles, starting from the administration of engineered cells, wherein CAR-T cells must encounter the correct chemotactic signals to traffic to the tumor in sufficient numbers. Additional obstacles arise from the hostile environment that cancers provide to CAR-T cells. Intense efforts have gone into tackling these pitfalls. However, we argue that some CAR-engineering strategies may risk missing the bigger picture, i.e., that a successful CAR-T-cell therapy must efficiently intertwine with the complex and heterogeneous responses that the body has already mounted against the tumor. Recent findings lend support to this model.