Tolerance is the so-called "Holy Grail" of transplantation, but achieving this state is proving a major challenge, particularly in the clinical setting. Even in rodents, the definition of true transplant tolerance is not applicable to many models, with late graft damage often occurring despite long-term graft survival. Hence the term "operational tolerance," based more on graft function and absence of exogenous immunosuppression, is being adopted. Although the most sought-after goal in this field is to intentionally induce this state in a controlled manner, translating protocols across species from rodents to the clinic, the current literature demonstrates that this is proving a formidable task. A complementary approach is to address transplant tolerance from a different angle, by studying tolerance-like phenomena that occur "unintentionally" in transplant patients after immunosuppressive drug weaning. Such spontaneous operational tolerance, which can take place after years of immunosuppression, is rare in kidney transplant recipients. However, determining exactly how this state arises and how it can be detected may make it possible to induce it in a greater number of patients and then to return to the drawing board to rationally design protocols that have a greater chance of clinical success. Moreover, the study of such patients should help in the identification of biomarkers of low immunological risk that could be used to select patients for potential weaning. Collaborative efforts through international networks, together with the application of newer and more powerful technologies to diagnostic, prognostic, and mechanistic research, may help transplanters to achieve this goal.