Accommodation refers to a condition in which a transplant (or any tissue) appears to resist immune-mediated injury and loss of function. Accommodation was discovered and has been explored most thoroughly in ABO-incompatible kidney transplantation. In this setting, kidney transplants bearing blood group A or B antigens often are found to function normally in recipients who lack and hence produce antibodies directed against the corresponding antigens. Whether accommodation is owed to changes in anti-blood group antibodies, changes in antigen or a change in the response of the transplant to antibody binding are critically reviewed and a new working model that allows for the kinetics of development of accommodation is put forth. Regardless of how accommodation develops, observations on the fate of ABO-incompatible transplants offer lessons applicable more broadly in transplantation and in other fields.