Ground-based Imaging Cherenkov Telescopes (IACTs) are gamma-ray detectors for non-thermal phenomena in the VHE range (GeV-TeV). Moved by the success of the current generation of experiments, a new great project of world-wide scale is being run, dubbed CTA (Cherenkov Telescope Array). Besides gamma-ray astronomy, IACTs can also be used as observatories for fundamental physics searches (dark matter, quantum gravity, axion-like particles), and even as cosmic-ray detectors (electrons, heavy nuclei), neutrino detectors (tau-induced showers) or detector for other exotic particles. In this presentation, I will briefly present the nature and statu of the CTA project and discuss some predictions for fundamental physic searches.