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In this paper, we consider non-parametric identification and estimation of truncated regression models in both cross-sectional and panel data settings. For the cross-sectional case, Lewbel and Linton (2002) considered non-parametric identification and estimation through continuous variation under a log-concavity condition on the error distribution. We obtain non-parametric identification under weaker conditions. In particular, we obtain non-parametric identification through discrete variation under a non-periodicity condition on the hazard function of the error distribution. Furthermore, we show that the presence of continuous regressors may lead to stronger identification results. Our non-parametric estimator is shown to be consistent and asymptotically normal, and outperforms that of Lewbel and Linton (2002) in a simulation study. For the panel data setting, we provide the first systematic treatment of non-parametric identification and estimation of the truncated panel data model with fixed effects by extending our treatment of the cross-sectional case. We also consider various other extensions. Copyright , Wiley-Blackwell.