Proceedings of the "XMM-Newton: the next decade", to appear in Astronomische Nachrichten.At low redshift (z<2), almost half of the baryons in the Universe are not found in bound structures like galaxies and clusters and therefore most likely reside in a Warm-Hot Intergalactic Medium (WHIM), as predicted by simulations. Attempts to detect WHIM filaments at cosmological distances in absorption towards bright background sources have yielded controversial results that I review here. I argue that a secure detection of absorption features by the WHIM is at the limit of the XMM-Newton capabilities, but feasible. A proper characterisation of the whole WHIM belongs to the realm of future X-ray missions.Financial support for this work has been provided by the Spanish Ministry of Education and Science under project ESP2006-13608-C02-01.Peer reviewed