The space between the galaxies in clusters of galaxies is filled with a hot tenous gas. Its high temperature (0.5-15 keV) is set by the the virialization process in the cluster's deep potential well, and the gas emits in X-rays predominantly through thermal Bremsstrahlung. This intracluster medium (ICM) is the main baryonic components of clusters and accounts for about 10% of the total dark matter dominated mass. While this is now wellestablished, it was not the case in the mid 70s, when the pioneering paper by Cavaliere & Fusco-Femiano (1976), which set the basis of the powerful β-model, was written.The idea of an ICM was proposed as early as 1959, but it took 10 years after its first detection in 1966 to definitively prove the existence of the hot ICM (see also Sarazin 1986; Biviano 2000, for a historical review). Limber (1959) stated that it is "rather likely that there is an appreciable quantity of intracluster gas pervading (...) clusters", primordial gas left over from galaxy formation, gas swept out of galaxies during galaxy collisions, or both. However, "it (was) not at all clear at (that) time whether one should expect the intracluster gas to be hot or cold". The first observational clue was the detection of M 87 in the Virgo cluster with the Geiger counters onboard an Aerobee rocket (Byram et al. 1966), which was also the first detection of an X-ray source associated with a cluster. The next major advance was made with Uhuru, the first satellite dedicated to X-ray astronomy, launched in 1970. Uhuru performed an all-sky X-ray survey and permitted longer observations of individual sources than with rockets experiments. This established that clusters are X-ray luminous sources and that the X-ray emission is extended and not time variable (e.g. Gursky et al. 1972, online).The detectors onboard Uhuru and rocket experiments were non-imaging proportional counters equipped with collimators to limit the field of view. Because of the crude spectral and spatial resolution (∼1 • ) of the detectors, the origin of the X-ray emission was ambiguous. Three possibilities were considered: 1) thermal bremsstrahlung from a hot tenuous gas; 2) inverse Compton (IC) scattering of CMB photons by relativistic electrons within the clusters; and 3) summed contributions of stellar sources (binaries or globular clusters). This was discussed very early by Felten et al. (1966) who correctly favored the thermal model on energetics arguments (unfortunately based on a spurious detection of the Coma cluster).In their paper, Cavaliere and Fusco-Femiano outlined several problems with the IC interpretation and, in particular, with the low value of the magnetic field implied by the ratio of the X-ray and Synchrotron radio luminosity. On the other hand, they emphasized that the IC emission is expected to stand out at energies above the thermal emission's exponential cut-off, E ∼ > 10 keV. The IC emission was indeed searched later on as an excess over the thermal emission in the hard X-ray band with Beppo-SAX, RXTE, and now Suzaku. Its level r...