Everywhere we look, the Universe is threaded with magnetism. These magnetic fields are surprisingly organised and coherent, and are vital to many of the fundamental processes that astronomers take for granted. However, the mechanisms that create and then sustain magnetism in the Universe are not understood, in no small part because magnetic fields are usually not directly observable. I will present innovative new observations of radio polarimetry and Faraday rotation, and will explain how these data sets provide a unique view of magnetic fields in the Milky Way, in distant galaxies, and in the intergalactic medium. I will conclude by showcasing the powerful new generation of radio telescopes that are at last fully opening the window to the magnetic Universe.