The detection of the radio signal from filaments in the cosmic web is crucial to distinguish possible magnetogenesis scenarios. We review the status of the different attempts to detect the cosmic web at radio wavelengths. This is put into the context of the advanced simulations of cosmic magnetism carried out in the last few years by our MAGCOW project. While first attempts of imaging the cosmic web with the MWA and LOFAR have been encouraging and could discard some magnetogenesis models, the complexity behind such observations makes a definitive answer still uncertain. A combination of total intensity and polarimetric data at low radio frequencies that the SKA and LOFAR2.0 will achieve is key to removing the existing uncertainties related to the contribution of many possible sources of signal along deep lines of sight. This will make it possible to isolate the contribution from filaments, and expose its deep physical connection with the origin of extragalactic magnetism.
