The Constant Elasticity of Substitution (CES) function is popular in several areas of economics, but it is rarely used in econometric analysis because it cannot be estimated by standard linear regression techniques. We discuss several existing approaches and propose a new grid-search approach for estimating the traditional CES function with two inputs as well as nested CES functions with three and four inputs. Furthermore, we demonstrate how these approaches can be applied in R using the add-on package micEconCES and we describe how the various estimation approaches are implemented in the micEconCES package. Finally, we illustrate the usage of this package by replicating some estimations of CES functions that are reported in the literature.