We present an in-depth investigation of the complex AGN-driven phenomena in cooling cluster cores which show some of the most spectacular signs of AGN-ICM interaction. We focus on M87 in the Virgo cluster and on Hydra A, where we find classical AGN-driven shocks with spectroscopically confirmed temperature and pressure jumps corresponding to consistent Mach numbers between 1.1 (M87) and 1.2-1.4 (Hydra A). We ran 1D hydrodynamic simulations of the large-scale shock in Hydra A to estimate its Mach number and energy. We also present 3D simulations, which show that a bulk flow of the ICM is needed to reproduce the observed shock front shape. Cool, metal-rich filaments associated with the radio lobes suggest moreover the crucial role of the AGN in uplifting the chemical elements produced by the central galaxy and transporting them into the ICM in both objects. We estimate the uplifted gas and iron mass in both M87 and Hydra A and discuss the enrichment mechanism and time-scales, as well as the energetics.