The existence of soft excess emission originating from clusters of galaxies, de ned as em- sion detected below 1 keV in excess over the usual thermal emission from hot intracluster gas (hereafter the ICM) has been claimed since 1996. Soft excesses are particularly - portant to detect because they may (at least partly) be due to thermal emission from the Warm-Hot Intergalactic Medium, where as much as half of the baryons of the Universe could be. They are therefore of fundamental cosmological importance. Soft excess emission has been observed (and has also given rise to controversy) in a number of clusters, mainly raising the following questions: