Summary:  Some human organ transplants deteriorate slowly over a period of years, often developing characteristic syndromes: transplant glomerulopathy (TG) in kidneys, bronchiolitis obliterans in lungs, and coronary artery disease in hearts. In the past, we attributed late graft deterioration to ‘chronic rejection’, a distinct but mysterious immunologic process different from conventional rejection. However, it is likely that much of chronic rejection is explained by conventional T-cell-mediated rejection (TMR), antibody-mediated rejection (AMR), and other insults. Recently, criteria have emerged to now permit us to diagnose AMR in kidney transplants, particularly C4d deposition in peritubular capillaries and circulating antibody against donor human leukocyte antigens (HLA). Some cases with AMR develop TG, although the relationship of TG to AMR is complex. Thus, a specific diagnosis of AMR in kidney can now be made, based on graft damage, C4d deposition, and donor-specific alloantibodies. Criteria for AMR in other organs must be defined. Not all late rejections are AMR; some deteriorating organs probably have smoldering TMR. The diagnosis of late ongoing AMR raises the possibility of treatment to suppress the alloantibody, but efficacy of the available treatments requires further study.