Galaxy clusters are the largest known virialized structures in the Universe and are therefore not only the largest physical laboratories in the Universe, galaxy clusters also inform and help constrain cosmology. The low surface brightness regions of galaxy cluster outskirts, beyond r500, seem to depart from hydrostatic equilibrium most likely due to cold gas clumps at large cluster radii, weakening accretion shocks, turbulence and cosmic rays, non-thermal pressure support from bulk motions, and electron-ion non-equilibrium. Galaxy clusters form and merge along and at the nodes of large-scale intercluster filaments. X-ray telescopes, particularly Suzaku with it’s low and stable particle background and more recently with increased time dedication from Chandra and XMM-Newton, have made it possible to reliably study galaxy cluster outskirts as far out as r200, where the outskirts meet and start to most noticeably, thus far, interact with the large-scale intercluster filament environment. These new studies in the X-ray are starting to shed light on cluster formation and enrichment scenarios, and on whether the departures, or non-departures, from hydrostatic equilibrium are correlated with the presence of intercluster filaments and the underlying thermodynamic processes that occur in this interface region. These relatively new studies will be discussed, with a focus on the more recent results of the Abell 3391/Abell 3395 intercluster filament, the Abell 98 intercluster filament, and the Abell 399/Abell 401 intercluster filament.