We present the work of an international team at the International Space Science Institute (ISSI) in Bern that worked together to review the current observational and theoretical status of the non-virialised X-ray emission components in clusters of galaxies. The subject is important for the study of large-scale hierarchical structure formation and to shed light on the missing baryon problem. The topics of the team work include thermal emission and absorption from the warm-hot intergalactic medium, non-thermal X-ray emission in clusters of galaxies, physical processes and chemical enrichment of this medium and clusters of galaxies, and the relationship between all these processes. One of the main goals of the team is to write and discuss a series of review papers on this subject. These reviews are intended as introductory text and reference for scientists wishing to work actively in this field. The team consists of sixteen experts in observations, theory and numerical simulations.
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