I review the current status of the comparison between observational properties of galaxy clusters and predictions from cosmological hydrodynamical simulations. My presentation focuses on the thermodynamical and chemical properties of the intra–cluster medium (ICM), as observed in the X–ray band. I finally discuss the properties of the galaxy population and their relation with the those of the hot diffuse gas. The emerging picture highlights that the current numerical description of galaxy clusters is able to account for several properties, such as the slope of the temperature profiles outside the core regions, the global chemical enrichment of the ICM and the color and luminosities for the bulk of the galaxy population. However, important discrepancies between observations and simulations are found, such as the thermal structure of cool cores and the colors of the brightest cluster galaxies. I emphasize that such two failures are two faces of the same problem, namely the difficulty of regulating gas cooling and star formation inside the most massive dark matter halos. This calls for the need of a source of energy feedback, which is not directly related to star formation, thus pointing towards AGN as a natural candidate for such a mechanism.