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Magnetic fields are a key ingredient of the extragalactic Universe on many different spatial scales, from individual galaxies and AGN to clusters of galaxies and large-scale structure, however they remain poorly understood. The coming years and decades will see a burst in our information and understanding of extragalactic magnetic fields due to the next generation of radio astronomy facilities, especially the SKA and its precursors, as well as major advances in MHD numerical simulations and algorithmic improvements to extract magnetism information from the databases. The Focus Meeting will bring together the observational, theoretical and computational communities to discuss the challenges and opportunities for understanding the magnetized universe from scales of galaxies to the cosmic web and connect information across the spectrum, to address the fundamental questions that are unanswered: - What are the magnetic field strength and structure? - How did magnetic fields form? - How did they evolve and how are they maintained? - How do they control the acceleration and dynamics of relativistic particles in astrophysical plasmas? - How do magnetic fields affect the evolution of thermal plasmas in galaxies and clusters? - How do magnetic fields illuminate otherwise invisible processes in the thermal plasma? - How do magnetic field contribute to the origins and evolution of structures in the Universe, from galactic to cosmic web scales?