We consider identiﬁcation and estimation of nonseparable sample selection models with censored selection rules. We employ a control function approach and discuss diﬀerent objects of interest based on (1) local eﬀects conditional on the control function, and (2) global eﬀects obtained from integration over ranges of values of the control function. We provide conditions under which these objects are appropriate for the total population. We also present results regarding the estimation of counterfactual distributions. We derive conditions for identiﬁcation for these diﬀerent objects and suggest strategies for estima-tion. We also provide the associated asymptotic theory. These strategies are illustrated in an empirical investigation of the determinants of female wages and wage growth in the United Kingdom.