Fundamental physics at the threshold of discovery

This thesis is divided into two parts: one driven by theory, the other by experiment. The first two chapters consider two model-building challenges: the little hierarchy of supersymmetry and the slowness of confinement in Randall-Sundrum models. In the third chapter, we turn to the question of determining the nature of fundamental physics at the TeV scale from LHC data. Crucial to this venture is a characterization for models of new physics. We present On-Shell Effective Theories (OSETs), a characterization of hadron collider data in terms of masses, production cross sections, and decay modes of new particles. We argue that such a description can likely be obtained from ≲ 1 year of LHC data, and in many scenarios is an essential intermediate step in describing fundamental physics at the TeV scale.