Abstarct: Today, statisticians are developing a variety of regression models beyond the mean regression where the purpose is to study different aspects of the conditional distribution of the response given some covariates. Primarily, we are interested in examining the effect of covariates on the tail of the distribution of the response variable; e.g., in the area of child health, physicians are interested in identifying the factors affecting child malnutrition; and in earthquake studies, researchers are seeking to know the conditions under which the most devastating earthquakes occur. Conventional models for achieving this goal are quantile regression models. The primary challenge of statistical inference in quantile regression models is their fitting to the data under study, which requires optimization of the objective function baxsed on linear programming. Considering this computational challenge, the class of expectile regression models is an appropriate alternative, particularly for spatial responses. In this thesis, we restate an expectile regression model for spatial responses and use a Bayesian approach to fit the model and implement inference. Also, we consider the modeling of nonlinear functions of covariates by using penalized splines and variable selection of covariates with linear effects by the spike and slab priors.