This paper studies identification and inference in transformation models with endogenous censoring. Many kinds of duration models, such as the accelerated failure time model, proportional hazard model, and mixed proportional hazard model, can be viewed as transformation models. I allow the censoring of duration outcome to be arbitrarily correlated with observed covariates and unobserved heterogeneity. I impose no parametric restrictions on the transformation function or the distribution function of the unobserved heterogeneity. In this setting, I partially identify the regression parameters and the transformation function, which are characterized by conditional moment inequalities of U-statistics. I provide an inference method for them by constructing an inference approach for the conditional moment inequality models of U-statistics. I apply the proposed inference method to evaluate the effect of heart transplants on patients’ survival time using data from the Stanford Heart Transplant Study.