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.