Nonseparable models are not additively separable in unobserved heterogeneity and therefore allow responses to policy interventions to vary across individuals with identical observed characteristics. This dissertation is a collection of three essays, each contributing to a different aspect of nonseparable econometrics models with endogeneity and sample selection. Binary response is a very important special case of nonseparable models, as it has many applications. In the first chapter, we consider a triangular simultaneous equations model with a binary outcome that is identified under a weak quantile restriction which allows for general forms of heteroskedasticity. The proposed two-step estimation procedure combines Horowitz's (1992) smoothed maximum score estimator in semiparametric binary response models with a control function approach to the endogeneity problem. Rates of convergence and the asymptotic distribution are derived. In a simulation study, we present the finite-sample performance of the estimator and illustrate advantages of the proposed approach by comparing with other alternatives. The second chapter provides an application of the methodology developed in Chapter 1 to an empirical context of female labor market participation with endogenous non-labor income. Using the data set extracted from the 2011 March Supplement to the US Current Population Survey, we find that, qualitatively similar to the probit estimates, accounting for endogeneity leads to a substantial increase in the magnitude of the non-labor income coefficient, being 62%~77% larger than that in the smoothed maximum score estimation. The coefficient estimates for different quantiles are considerably different, implying that strong full conditional independence may fail or heteroskedasticity may be present in the data set considered. In the third chapter, we discuss what features of sample selection models without imposing additivity can be identified under various restrictions. We focus on a nonparametric nonseparable sample selection model with possibly endogenous regressors. Using a control function approach, we provide identification results and develop a three-step nonparametric estimator for the average structural function given selection. Convergence rates are derived. A simulation study compares the numerical performance of the proposed estimator with Das, Newey, and Vella (2003) estimator and Heckman's two-step estimator under correct specifications and misspecifications.