X-ray and radio observations of galaxy clusters have revealed a wealth of structures in association with extragalactic radio sources. Structures in the form of large-scale cavities and weak shocks provide a reliable gauge of the energy output of extragalactic radio jets launched by AGNs. Furthermore, they place interesting constraints on the nature of AGN outflows, especially on large scales. We will present 3-D MHD simulations of jets/lobes in the ICM and compare them with ~70 X-ray cavities as well as individual jet/lobe sources. In addition, we will present cosmological MHD simulations of galaxy cluster formation with AGN jets/lobes feedback and its implications for 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. We quantify the available turbulent kinetic energy and nonlinear cascade rates. This turbulence excites a small-scale dynamo process that transports 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. We describe the properties of magnetic fields, including their strength, spatial distribution, power spectra and saturation mechanism. These simulations can be compared with observations made by VLA, LOFAR, and E-VLA.