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We review the present theoretical and numerical understanding of magnetic field amplification in cosmic large-scale structure, on length scales of galaxy clusters and beyond. Structure formation drives compression and turbulence, which amplify tiny magnetic seed fields to the microGauss values that are observed in the intracluster medium. This process is intimately connected to the properties of turbulence and the microphysics of the intra-cluster medium. Additional roles are played by mergerdoi:10.1007/s11214-018-0556-8 fatcat:t3yu4j2r6jdjvboplxles7j44u