This AGRODEP Technical Note provides a literature review on the topic of estimation of demand and supply elasticities. To this end, it starts the discussion by summarizing the main facets of production theory and consumer theory to introduce the concept of elasticities, with examples of di fferent types of elasticities most utilized in the literature. Next, it discusses the identi fication problem in estimating elasticities, i.e. the issue of having to solve for unique values of the parameters of the structural model from the values of the parameters of the reduced form of the model. It summarizes various methodologies employed in the literature to solve this problem and gives practical examples. These solutions include, but are not limited to, using instrumental variables, adopting a recursive structure, holding demand constant, and imposing inequality constraints in order to restrict the domain of estimates.