A semiparametric regression model consists of parametric explanatory part of the response as well as nonparametric regression function of one or more variable(s) interpreting the response. The basic semiparametric regression model involves a linear function of a single parametric covariate as well as an unknown but preferably nonlinear function of a single nonparametric covariate. The scope of this chapter is to provide estimation techniques for the nonparametric regression function, including kernel smoothing, spline smoothing and local linear as well as polynomial smoothing. Also, the estimation of the parametric explanatory part of the response can be done using the technique by Robinson (1988). The asymptotic properties of the estimators of the parametric and nonparametric regression functions need to be discussed to furnish a consistent prediction of the response.