For more than three decades, empirical analysis of stochastic dominance was restricted to settings with mutually exclusive choice alternatives. In recent years, a number of methods for testing efficiency of diversified portfolios have emerged, following the works of Kuosmanen (2001, 2004) and Post (2003). The proposed methods differ in terms of their objectives, information content of the results, as well as their computational complexity. Unfortunately, advantages and disadvantages of alternative approaches have not been duly recognized. Moreover, this emerging literature is plagued with a number of incorrect or misleading arguments and sometimes clear mathematical errors. The purpose of this paper is to develop a unified methodological framework to bridge the gap between different approaches. To this end, we critically review some of the main developments in this emerging literature, evaluate the advantages and disadvantages of the alternative approaches, and identify some errors.