Bivalent CTLA4 homodimers bridge bivalent B7.1 homodimers to form an unusually stable signaling complex. Blocking B7/CD28 interactions with monoclonal antibodies or soluble receptors results in immunosuppression and enhanced allograft survival, while B7/CTLA-4 blockade results in enhanced antitumor immune responses. The interaction of co-stimulatory antigen molecules on T cells with B7 molecules on presenting cells plays an important role in the activation of naive T cells. Consequently, agents that disrupt these interactions should have applications in treatment of transplant rejection as well as autoimmune diseases.