Astroparticle physics with the IceCube neutrino telescope

Cosmic rays were discovered exactly 100 years ago. Their origin remains a mystery. The IceCube Neutrino Observatory, the largest neutrino telescope in the world, has been recently completed at the South Pole. It provides a unique view of the Universe and sever tests of cosmic ray physics. In this talk, we will review the recent results obtained with IceCube concerning Gamma-ray Burst, galactic cosmic ray accelerators and ultra-high energetic particles. Moreover, based on the IceCube data, we search indirectly for dark matter and we study the properties of neutrinos. The status of these searches will be also reviewed.