In galaxy clusters, non-thermal components such as magnetic field and
high energy particles keep a record of the processes acting since early
times till now. These components play key roles by controlling transport
processes inside the cluster atmosphere and beyond and therefore have
to be understood in detail by means of numerical simulations. The complexity
of the intra cluster medium revealed by multi-frequency observations
demonstrates that a variety of physical processes are in action and
must be included properly to produce accurate and realistic models.
Confronting the predictions of numerical simulations with observations
allow to validate different scenarios about origin and evolution of
large scale magnetic fields and allow to investigate their role in
transport processes of cosmic rays.