This chapter demonstrates how majorization theory provides a powerful tool for the study of robustness of many important models in economics, finance, econometrics, statistics, risk management, and insurance to heavy-tailedness assumptions. The majorization relation is a formalization of the concept of diversity in the components of vectors. Over the past decades, majorization theory, which focuses on the study of this relation and functions that preserve it, has found applications in disciplines ranging from statistics, probability theory, and economics to mathematical genetics, linear algebra, and geometry (see Marshall et al. 2011, and the references therein).