This dissertation focuses on the research on the semiparametric and nonparametric estimation of Tobit models such as the truncated and censored regression models, bivariate Tobit models, and censored sample selection models. The applied methods are not traditional compared with the moment-based approaches in the literature on the estimation of the models with limited dependent variables. The dissertation contains four chapters. The first chapter provides a new semiparametric estimator for the coefficients in the truncated regression model based on the least-squares estimation of the conditional survival function for the truncated dependent variable in contrast with the moment-based semiparamtric estimation approach in the literature. Identification conditions about the error term and the regressors for the estimation are also presented, where the non-periodic condition for the hazard function of the error term is much weaker than the log concavity condition for the density function of the error term in the literature. The proposed estimator is shown to be root-n-consistent and asymptotically normal by the theory of U-statistic from Sherman (1994) and the empirical process from Pakes and Pollard (1989). The simulation study shows that our estimator performs well and better than the estimators in the literature in the designs. The method in the chapter can also be generalized to the semiparametric estimation for censored regression models. The second chapter proposes a semiparametric estimation for the bivariate Tobit model. This model was introduced by Amemiya (1974) who gave an estimation based on the joint normality assumption on the error terms. The limitation of the normality assumption and the inefficiency of the Amemiya’s estimator motivate us to semiparametrically estimate the model. So far, this problem has not been studied in the literature. Instead of starting from a simple relationship between the first and second moments of the dependent variables as Amemiya (1974), we begin with the conditional ...