The existence of X-ray cavities coincident with radio emission, radio relics and halos imply that the ICM is filled with non-thermal particles (i.e., cosmic rays) and magnetic fields. The morphology of the cavities suggest that viscosity and/or magnetic fields are important. Transport processes can also be responsible for the dissipation of the energy in the sound waves generated by the AGN. It is for these reasons that we need to go beyond the ideal hydrodynamical approach to study the ICM. I will discuss some of the above processes in the context of numerical simulations of the ICM. In particular, I will describe: (1) how dynamically unimportant magnetic fields can stabilize the AGN bubbles against disruption via the "magnetic draping" effect, (2) the simulations of the diffusion of non-thermal particles from the bubbles and its consequences for the heating of the ICM, (3) our recent simulations of the plasma instabilities driven by the anisotropic diffusion of cosmic rays. I will discuss the diffusion rates of cosmic rays from the cool cores and the implications for the gas heating and the central metallicity dips seen in some clusters.