The ground-based gamma-ray observatory CTA (Cherenkov Telescope Array) will span over three decades in energy, from ~20 GeV to ~100 TeV, with unprecedented sensitivity. The array will cover an area of several square km with three different sizes of wide field of view telescopes. This configuration allows measurements on the charged component of cosmic rays, deriving composition and spectrum of heavy nuclei up to the knee (3 PeV) and of electron/positrons up to several TeVs. CTA will also address fundamental and exotic physics issues, such the search of signatures from dark matter candidates, violation of Lorentz invariance and detection of air showers from tau-leptons. We will briefly describe these topics.