Accommodation refers to the acquired resistance of a graft to immune-mediated injury. It is typically observed after antibodies that would cause rejection of a graft are removed from a recipient and then later return. In addition to being induced in this manner, accommodation can occur spontaneously, without depleting antibodies. Indeed, we postulate spontaneous accommodation may be the most common outcome of clinical organ transplantation. The paper reviews the current understanding of accommodation, emphasizing recent advances and important questions. Among the recent advances are the discoveries of potentially broader relevance of accommodation for biology and immunology and pathways by which accommodation may be achieved. To investigate these pathways and to understand how accommodation begins and how it evolves, clinical organ transplants might offer a useful and incisive model.