Chimeric antigen receptor (CAR) T cells use re-engineered cell surface receptors to specifically bind to and lyse oncogenic cells. Two clinically approved CAR-T-cell therapies have significant clinical efficacy in treating CD19-positive B cell cancers. With widespread interest to deploy this immunotherapy to other cancers, there has been great research activity to design new CAR structures to increase the range of targeted cancers and anti-tumor efficacy. However, several obstacles must be addressed before CAR-T-cell therapies can be more widely deployed. These include limiting the frequency of lethal cytokine storms, enhancing T-cell persistence and signaling, and improving target antigen specificity. We provide a comprehensive review of recent research on CAR design and systematically evaluate design aspects of the four major modules of CAR structure: the ligand-binding, spacer, transmembrane, and cytoplasmic domains, elucidating design strategies and principles to guide future immunotherapeutic discovery.