Modern hydrodynamical simulations offer nowadays a powerful means to trace the evolution of the X-ray properties of the intra-cluster medium (ICM) during the cosmological history of the hierarchical build up of galaxy clusters. In these lectures I review the current status of these simulations and how their predictions fare in reproducing the most recent X-ray observations of clusters. After briefly discussing the shortcomings of the self-similar model, based on assuming that gravity only drives the evolution of the ICM, I discuss how the processes of gas cooling and non-gravitational heating are expected to bring model predictions into better agreement with observational data. I then present results from the hydrodynamical simulations, performed by different groups, and how they compare with observational data. As terms of comparison, I use X-ray scaling relations between mass, luminosity, temperature and pressure, as well as the profiles of temperature and entropy. The results of this comparison can be summarised as follows: a) simulations, which include gas cooling, star formation and supernova feedback, are generally successful in reproducing the X-ray properties of the ICM outside the core regions; b) simulations generally fail in reproducing the observed “cool core” structure, in that they have serious difficulties in regulating overcooling, thereby producing steep negative central temperature profiles. This discrepancy calls for the need of introducing other physical processes, such as energy feedback from active galactic nuclei, which should compensate the radiative losses of the gas with high density, low entropy and short cooling time, which is observed to reside in the innermost cluster regions.