Abstract: Theories comprehensively addressing the origin and robustness of the observed hierarchical structure of particle physics face significant challenges from the non-appearance of new particles, explicitly in LHC searches or virtually within an increasingly powerful and precise array of low-energy experiments. I will describe efforts to combine the most compelling theoretical mechanisms for generating particle hierarchies and assessing our prospects for experimental discovery in the coming generation, in particular showing how supersymmetry and compositeness can reinforces each other’s shortcomings. I will also illustrate how phenomenologically important questions relate to hard but interesting questions in strongly-coupled quantum field theory.