Prompt by an increasing interest by climate change modelers, a rich literature estimating elasticities of substitution in a nested CES production framework has recently developed. This article reviews such literature. We critically describe the nesting structures, estimation approaches, data sources and aggregation, econometric techniques, and types of substitution elasticities used by previous literature, to offer a comprehensive description of the various options available to a researcher attempting this estimation. We also provide suggestions for potential improvements to the estimation process. In particular, we warn researchers to use CES production functions with caution in empirical applications given their restrictive build-in assumptions.