Humoral immunity, as a cause of damage to blood vessels, poses a major barrier to successful transplantation of organs. Under some conditions, humoral immunity causes little or no damage to an organ graft. We have referred to this condition, in which a vascularized graft functions in the face of humoral immunity directed against it, as "accommodation." In this paper, we review changes in the graft and in the host that may account for accommodation, and we consider that what we call accommodation of organ grafts may occur widely in the context of immune responses, enabling immune responses to target infectious organisms without harming self-tissues.