  In the past, different works based on numerical simulations have been
presented to explain magnetic fields (MFs) in the large scale structure and
within galaxy clusters. In this review, I will summarize the main findings
obtained by different authors and - even if many details are still unclear - I
will try to construct a consistent picture of our interpretation of large-scale
magnetic fields based on numerical effort. I will also sketch how this is
related to our understanding of radio emission and summarize some arguments
where our theoretical understanding has to be improved to match the
observations.
