Similarly to the interstellar medium, the intergalactic medium (IGM) is likely to be strongly affected by non-thermal processes. I will start with the epoch of reionization, during which the IGM was ionized by the UV radiation produced by the first stars and quasars which formed at redshifts z>6. Outflows from quasars magnetize the IGM at all redshifts. As a result, the shocks produced by converging flows during the formation of large scale structure in the IGM, accelerate electrons to relativistic energies and become visible in the radio regime through their synchrotron emission and in the gamma-ray regime through their inverse-Compton scattering of the microwave background photons. During transient episodes of strong mergers, X-ray clusters should therefore appear as extended radio or gamma-ray sources on the sky.