  We study the challenges to detect the cosmic web at radio wavelengths with
state-of-the-art cosmological simulations of extragalactic magnetic fields. The
incoming generation of radio surveys operating at low frequency, like LOFAR,
SKA-LOW and MWA will have the best chance to detect the large-scale, low
surface brightness emission from the shocked cosmic web. The detected radio
emission will enable to constrain the average magnetisation level of the gas in
filaments and the acceleration efficiency of electrons by strong shocks. In
case of detections, through statistical modelling (e.g. correlation functions)
it will be possible to discriminate among competing scenarios for the
magnetisation of large-scale structures (i.e. astrophysical versus primordial
scenarios), making radio surveys an important probe of cosmic magnetogenesis.
