This thesis contributes in several ways to the existing knowledge on estimation of truncated, censored, and left truncated right censored (LTRC) regression models. Three new semiparametric estimators are proposed, allowing for asymmetric error distributions. A bootstrap method for estimation of the covariance matrix of the quadratic mode estimator (QME) is proposed and studied. In addition, finite sample properties of estimators for truncated, censored, and LTRC data are studied within simulation studies and applications with real data. The first paper consists of a simulation study of the QME and other estimators of truncated regression models. The paper contributes with results suggesting the bootstrap technique being potentially useful for estimation of the QME covariance matrix. In the second paper estimators of truncated and censored semiparametric regression models are proposed. These estimators are generalizations of the QME and the winsorized mean estimator (WME) by allowing asymmetric ``trimming'' of observations. Consistency and asymptotic normality of the estimators are shown. By combining the two moment restrictions used to derive the estimators in the second paper, a consistent estimator of LTRC regression models is proposed in the third paper. The fourth paper contains an application where LTRC interpurchase intervals of cars are analysed. Results regarding the interpurchase behaviour of consumers are provided, as are results on estimator properties.