There is disclosed compositions and methods relating to or derived from anti-CTLA4 antibodies. More specifically, there is disclosed fully human antibodies that bind CTLA4, CTLA4-antibody binding fragments and derivatives of such antibodies, and CTLA4-binding polypeptides comprising such fragments. Further still, there is disclosed nucleic acids encoding such antibodies, antibody fragments and derivatives and polypeptides, cells comprising such polynucleotides, methods of making such antibodies, antibody fragments and derivatives and polypeptides, and methods of using such antibodies, antibody fragments and derivatives and polypeptides, including methods of treating a disease requiring either stimulation of immune responses or suppression. Stimulation is achieved using antibodies that block binding of human CTLA4 to human B7 and diseases amenable to treatment by stimulation and augmentation of prolonging of immune responses include cancers of the prostate, kidney, colon, lung or breast; pathogenic infections; diseases associated with the CNS e.g. amyloidogenic diseases including Alzheimer's disease; and diseases with inflammatory or allergic components. Diseases amenable to treatment include graft versus host disease, host versus graft disease, allergy, autoimmune diseases and other inflammatory diseases.