The research activities of our group focus on the emergent physical behavior of strongly correlated electron systems. Prominent examples of fascinating phenomena arising from electronic correlations are high-temperature superconductivity or quantum criticality. The impressive technological advancements in the device fabrication strongly stimulated the exploration of new phases of matter. At the same time, the development of new many-body techniques for their theoretical description became a central aspect of the forefront research. In recent years, various renormalization-group approaches lead to significant progress in the understanding of correlated electron systems in and out of equilibrium. In particular, by means of these approaches and of their most recent developments, we investigate the fundamental mechanisms underlying the physical behavior of model systems for materials, cold atomic gases and nanostructures.