  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
this paper we 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, we discuss how the
processes of gas cooling and non-gravitational heating are expected to bring
model predictions into better agreement with observational data. We then
present results from the hydrodynamical simulations, performed by different
groups, and how they compare with observational data. As terms of comparison,
we 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 regions of galaxy clusters.
