The hallmarks of the adaptive immune response are specificity and memory. The cellular response is mediated by T cells which express cell surface T cell receptors (TCRs) that recognize peptide antigens in complex with major histocompatibility complex (MHC) molecules on antigen presenting cells (APCs). However, binding of cognate TCRs with MHC-peptide complexes alone (signal 1) does not trigger optimal T cell activation. In addition to signal 1, the binding of positive and negative costimulatory receptors to their ligands modulates T cell activation. This complex signaling network prevents aberrant activation of T cells. CD28 is the main positive costimulatory receptor on naı¨ve T cells; upon activation, CTLA4 is induced but reduces T cell activation. Further studies led to the identification of additional negative costimulatory receptors known as checkpoints, e.g. PD1. This review chronicles the basic studies in T cell costimulation that led to the discovery of checkpoint inhibitors, i.e. antibodies to negative costimulatory receptors (e.g. CTLA4 and PD1) which reduce tumor growth. This discovery has been recognized with the award of the 2018 Nobel prize in Physiology/Medicine. This review highlights the structural and functional roles of costimulatory receptors, the mechanisms by which checkpoint inhibitors work, the challenges encountered and future prospects.