Clusters of galaxies are next to quasars, the most luminous X-ray sources in the Universe with radiation powers of the order of 1043–1046 erg s−1. The first detection of a cluster source was made with M87 in 1966 by Byram et al. [30], and 5 years later also the massive nearby clusters in the constellations Coma Berenices and Perseus were detected by Gursky et al. [71] and Fritz et al. [65]. With the use of the Uhuru satellite, the extended nature of the cluster X-ray sources could be established [85]. It turns out that the diffuse X-ray emission from clusters originates in a hot intracluster plasma with temperatures of several ten Million degrees, which radiates the bulk of its thermal radiation in the soft X-ray regime. As the hot plasma is tracing the shape of the cluster, the X-ray appearance provides us with information on the cluster structure. The soft X-ray band in which clusters radiate is fortunately also the wavelength regime for which X-ray telescopes with imaging optics provide us with a detailed picture of the X-ray sky. Therefore, galaxy clusters are among the most rewarding and informative objects for X-ray imaging studies. With the very rapid evolution of X-ray observational techniques, the X-ray studies of galaxy clusters have also experienced a breathtaking evolution. X-ray observations have provided us with a wealth of detailed knowledge on the cluster structure, composition, and formation history as well as on the statistics of the galaxy cluster population. Most of our current systematic understanding of galaxy clusters, the cluster population, and the link to the formation of large scale structure and the underlaying cosmological model is based on X-ray observations. And the importance of X-ray astronomy for cluster research is still increasing. At this moment we can provide an overview on galaxy cluster research in X-rays where the advanced X-ray observatories Chandra and XMM-Newton have unfolded and demonstrated their full capabilities. This field of research is so rich, however, that such a contribution can only provide an illustrative tour through the field rather than a comprehensive review. In particular, the references give only examples of publications as a first starting point for a literature search and cannot be complete due to space limitations. The most detailed introduction to X-ray studies of galaxy clusters is given by the review of Sarazin [127], which is now outdated in its detailed description of observational results but still provides an excellent astrophysical background. More specialized recent reviews focus on X-ray cluster appearance by Forman and