This paper reviews the recently emerging procedures for testing two or more econometric models when each belongs to a separate parametric family, i.e., the models are non-nested. The concepts of nested, partially non-nested, and globally non-nested hypotheses are formally defined and illustrated with the help of several simple examples in the fields of economics and statistics. To justify the emergence of such specialized procedures, the limitations of existing classical procedures when applied to non- nested hypotheses are duly explained. The modified likelihood ratio approach of Cox, various tests based on artificial embedding approach, and tests based on the instrumental variable are discussed as the alternative procedures for testing non-nested hypotheses. The paper provides an up-to-date reference of various empirical applications and summarizes the available evidence on the statistical properties of various non-nested test statistics.