More than 20 years have passed since the radical concept was first proposed that target recognition by T lymphocytes need not lead to immune system activation resulting in that target’s destruction. Rather, it was proposed that T-cell activation required antigen recognition but also a simultaneous “costimulatory” signal. A corollary of the hypothesis was that antigen recognition without costimulatory signals would not only fail to activate the immune response against that target but would also permanently and specifically impair the anti-target immune response to produce an immunologic state called “anergy.” During the past 20 years, research directed to test the costimulatory or “two-signal” hypothesis has generated a prodigious volume of data, much of it dramatic with regard to possible transplant therapies. During the same interval, however, it has become evident that the two-signal hypothesis as initially proposed was at best oversimplified. The history of costimulation research is discussed here along with current research emphasizing areas where much remains to be understood.