I will describe and update the comprehensive theoretical frameworks capable of explaining the hierarchical structure of particle physics and how they present diverse ambitious targets for high-energy colliders. These targets include WIMP dark matter and SUSY, Particle Compositeness and the origins of flavor/CP-violation, baryogengesis, and Grand Unification. And yet, BSM physics is very strongly constrained by a host of precision low-energy tests (and LHC searches) for reasons that lie in the special structure of the standard model itself. I will explain the known principles that can evade these constraints and allow rich BSM physics to fall into collider reach, and how they affect the phenomenology.