This thesis looks at different aspects of robustness in the analysis of structural models. The first chapter illustrates the importance of functional form specification for correct inferences on the non-parametric components of a semi-parametric model. Empirical results are provided using the German Socio Economic Panel data. The second chapter takes the quantile regression, conditional and unconditional, as robust methods to analyze the effect of minimum wages on the entire wage distribution for four developing countries: Brazil, Mexico, Indonesia and India. In the last chapter we focus on the robust estimation of the non-linear parameters in the context of Small Area Estimation and we propose new bias calibration methods. The performance of these methods is compared with the existing competitors in the literature. These methods mostly outperform the others specially in cases when we are dealing with a heavy-tailed and highly skewed distribution, such as the distribution of income or expenditure.