  The distribution of chemical elements in the hot intracluster medium (ICM)
retains valuable information about the enrichment and star formation histories
of galaxy clusters, and on the feedback and dynamical processes driving the
evolution of the cosmic baryons. In the present study we review the progresses
made so far in the modelling of the ICM chemical enrichment in a cosmological
context, focusing in particular on cosmological hydrodynamical simulations. We
will review the key aspects of embedding chemical evolution models into
hydrodynamical simulations, with special attention to the crucial assumptions
on the initial stellar mass function, stellar lifetimes and metal yields, and
to the numerical limitations of the modelling. At a second stage, we will
overview the main simulation results obtained in the last decades and compare
them to X-ray observations of the ICM enrichment patterns. In particular, we
will discuss how state-of-the-art simulations are able to reproduce the
observed radial distribution of metals in the ICM, from the core to the
outskirts, the chemical diversity depending on cluster thermo-dynamical
properties, the evolution of ICM metallicity and its dependency on the system
mass from group to cluster scales. Finally, we will discuss the limitations
still present in modern cosmological, chemical, hydrodynamical simulations and
the perspectives for improving the theoretical modelling of the ICM enrichment
in galaxy clusters in the future.
