Majority of galaxies reside in groups and clusters where they are understood to evolve also through galaxy-galaxy interactions. Multiple mergers at the core of galaxy groups can develop a luminosity deficiency or gap, which is quantified as the difference between the luminosity of the two brightest galaxies in groups and clusters. This observable carries important information about the evolution of galaxy groups, for instance, there are indications that collapsed groups with a large luminosity gap, known as fossil groups, are associated with the halos that are relatively old. In a series of recent studies, employing X-ray, optical and radio observations complemented by cosmological simulations, we have utilised the luminosity gap to probe the formation scenarios for galaxies and specially the most luminous galaxies in groups and clusters, introduce a powerful age-date routine for galaxy groups, and also obtain clues about the AGN activities and the IGM heating.