I will be discussing weak-scale extensions of the Standard Model which automatically preserve its accidental and approximate symmetry structure at the renormalizable level and which are hence invisible to low-energy indirect probes. By requiring the consistency of the effective field theory up to scales of 10^15 GeV or higher and after applying cosmological constraints, one arrives at a finite set of possibilities that I will analyze in detail. One of the most striking signatures of this framework is the presence of new charged and/or colored states which can be efficiently produced in high-energy particle colliders and which are stable on the scale of detectors.
