  Detecting the thermal and non-thermal emission from the shocked cosmic gas
surrounding large-scale structures represents a challenge for observations, as
well as a unique window into the physics of the warm-hot intergalactic medium.
In this work, we present synthetic radio and X-ray surveys of large
cosmological simulations in order to assess the chances of jointly detecting
the cosmic web in both frequency ranges. We then propose best observing
strategies tailored for existing (LOFAR, MWA and XMM) or future instruments
(SKA-LOW and SKA-MID, ATHENA and eROSITA). We find that the most promising
targets are the extreme peripheries of galaxy clusters in an early merging
stage, where the merger causes the fast compression of warm-hot gas onto the
virial region. By taking advantage of a detection in the radio band, future
deep X-ray observations will probe this gas in emission, and help us to study
plasma conditions in the dynamic warm-hot intergalactic medium with
unprecedented detail.
