This paper establishes the asymptotic normality of series estimators for nonparametric regression models. Polynomial series estimators, trigonometric series estimators, and Gallant's Fourier flexible form estimators are prime examples of the estimators covered by the results. The results apply to a wide variety of estimands in the regression model under consideration, including derivatives and integrals of the regression function. The errors in the model may be homoskedastic or heteroskedastic. The paper also considers series estimators for additive interactive regression (AIR), partially linear regression, and semiparametric index regression models and shows them to be consistent and asymptotically normal. All of the consistency and asymptotic normality results in the paper follow from one set of general results for series estimators.