Many strongly correlated systems are at the forefront of experimental and theoretical research in condensed matter physics, among them High Temperature Superconductors, Manganites, and Vanadates. These materials are modeled by simplified theoretical descriptions like the Heisenberg, Hubbard, and Kondo models and their combinations. Several kinds of dynamical degrees of freedom, including charge, spin, and lattice modes, often interact in these systems. Theoretical investigations in these areas are extremely challenging, since the importance of strong correlations causes most traditional methods to work badly or to fail altogether. Our group concentrates on applying unbiased numerical approaches at zero and finite temperature like Exact Diagonalization, Determinantal and Loop Cluster Quantum Monte Carlo, and DMRG, together with supporting analytical approaches. We put special emphasis on developing and improving new techniques without systematical errors, in order to extend the accessible range of models and physics, and to simultaneously study the important interplay of different dynamical degrees of freedom. We have, e.g., been investigating Transport properties and charge response in Vanadium ladder systems, CMR and spin response in Manganites, Screening and transport in Hubbard models, Spectra of Heisenberg ladder systems, and Spin dynamics in classical spin systems.