A remarkable discovery made by 20th century astronomers was that the Universe is threaded with magnetic fields. Furthermore, these magnetic fields typically do not have a random, tangled, morphology, but are surprisingly organised and coherent. However, the processes that create and then sustain this large-scale magnetism are not yet understood. I will present innovative new observations of radio polarisation and Faraday rotation, and will explain how these data sets provide a unique view of magnetic fields in interstellar gas, in the Milky Way, and in distant galaxies. These experiments pave the way to the opening of the full magnetic Universe with the next generation of radio telescopes, culminating in the Square Kilometre Array.