Immune checkpoint blockade is able to induce durable responses across multiple types of cancer, which has enabled the oncology community to begin to envision potentially curative therapeutic approaches. However, the remarkable responses to immunotherapies are currently limited to a minority of patients and indications, highlighting the need for more effective and novel approaches. Indeed, an extraordinary amount of preclinical and clinical investigation is exploring the therapeutic potential of negative and positive costimulatory molecules. Insights into the underlying biological mechanisms and functions of these molecules have, however, lagged significantly behind. Such understanding will be essential for the rational design of next-generation immunotherapies. Here, we review the current state of our understanding of T-cell costimulatory mechanisms and checkpoint blockade, primarily of CTLA4 and PD-1, and highlight conceptual gaps in knowledge. This review provides an overview of immune checkpoint blockade therapy from a basic biology and immunologic perspective for the cancer research community.