Cosmological simulations of magnetic fields in galaxy clusters show that remarkable agreement between simulations and observations of Faraday rotation and radio haloes can be achieved assuming that seed fields of similar to 10(-9) G were present at redshifts similar to 15-20. The structure of the seed field is irrelevant for the final intracluster field. On average, the field grows exponentially with decreasing cluster redshift, but merger events cause steep transient increases in the field strength. Typical field-reversal,scales are of order 50h(-1)kpc. In most cases, the intracluster fields are dynamically unimportant. Assuming secondary electron models, the average structure of cluster radio haloes can naturally be reproduced.