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Galaxy groups consist of a few tens of galaxies bound in a common gravitational potential and contain a significant fraction of the overall universal baryon budget. Therefore, they are key to our understanding of how the bulk of matter in the Universe accretes and forms hierarchical structures and how different sources of feedback affect their gravitational collapse. However, despite their crucial role in cosmic structure formation and evolution, galaxy groups have received less attention compared to massive clusters. This is perhaps in part due to their rarity in being observed and properly characterized. With the advent of eROSITA, many thousands of galaxy groups will be detected by X-ray, complementing optical and SZ coverage. In this Special Issue we collected and organized the latest developments in our understanding of these systems and present future prospects from both observational and theoretical points of view.

fossil galaxy groups --- galaxy clusters --- galaxy groups --- X-ray and optical observations --- hydrodynamical simulations --- intragroup medium/plasma --- active galactic nuclei --- black holes --- elliptical galaxies --- active nuclei --- X-ray observations --- hydrodynamical and cosmological simulations --- galaxies:abundances --- galaxies:clusters:intracluster medium --- X-rays:galaxies --- galaxy surveys --- UV observations --- cosmological parameters --- n/a