In this thesis, we present an expanded account of Small Area Estimation with Linear and Generalized Linear Mixed-Effects Models based on an article by Chambers and Tzavidis (2008). Small area estimation techniques typically rely on mixed models containing random area effects to characterize between area variability. In contrast, an approach to small area estimation based on sensitivity function and M-quantiles has been described. This approach avoids conventional Normal assumption and problems associated with specification of random effects. These assumption are complicated to calculate some estimators and also outlier may effect on unbiasness or efficiency of small area estimators, therefore robust approach could help us to dominate on these problems. In this thesis endeavor to describe not only mixed models and its relation to small area estimation but also robust approach for small area problems based on both bounded influence function and M-quantiles regression. Small area models have been studied in the literature to obtain empirical best linear unbiased predictors for small area means. Although this ltr"