For billions of years, magnetic fields have regulated the feedback vital for returning matter to the interstellar and intergalactic medium. However, the evolution, structure and origin of magnetism on the largest scales are still open problems. I will review recent results that showcase the unique view of magnetic fields provided by radio astronomy. I will then explain how the Square Kilometre Array and other future radio facilities can provide data that will reveal what cosmic magnets look like, how they formed, and what role they have played in the evolving Universe.