X-ray and radio observations of galaxy clusters have revealed a wealth of structure in their hot halos associated with extragalactic radio sources. Structures in the form of large scale cavities and weak shocks provide a reliable gauge of the mechanical output of extragalactic radio jets launched by AGNs. The energies involved range between 1E57 to 1E62 ergs. Furthermore, the morphology and properties of cavities have given strong constraints on the nature of AGN outflows, especially on large scales. We will present cosmological magnetohydrodynamic (MHD) simulations of AGN feedback in galaxy clusters, emphasizing the important role of magnetic fields in carrying the AGN energy and in the cavity formation. We will also discuss the origin and energetics of the cluster-wide magnetic fields. We demonstrate that the ICM turbulence is excited and sustained by the frequent mergers during the cluster formation. This turbulence excites a dynamo process that transports, spreads, and amplifies the fields originated from the radio jet/lobe system. This process could be the primary process of populating the whole cluster with magnetic fields.