As we enter the LHC era, no indirect searches for physics beyond the Standard Model have given us any conclusive evidence of new particles at the TeV scale. If there is new physics within the reach of the LHC, it appears to hide itself well from low energy probes. Therefore it is interesting to ask what types of TeV-scale physics can be consistent with the null results of flavor and precision electroweak experiments without requiring artificial fine-tuning. In this talk I will derive insight from the structure of QCD at energies below the confinement scale and argue for the plausibility of a class of theories with strong dynamics at the TeV scale. These theories naturally have minimal impact on flavor and precision electroweak observables, and yet they give rise to spectacular signatures at the LHC such as resonant production, massive stable particles, and multi-photon final states among others. Several final states occurring in these theories are currently being searched for by groups within ATLAS and CMS.