Abstract: Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process, due to Alfred Young, that expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. It has been a long-standing open problem to give a non-iterative, closed formula for this straightening process. In this talk I will give such a formula, as well as a simple combinatorial description of the coefficients that arise. Moreover, an interpretation of these coefficients in terms of paths in a directed graph will be explored. I will end by discussing a surprising application of this formula towards finding multiplicities of irreducible representations in certain plethysms and how this relates to Foulkes' conjecture.