"Strongly correlated materials exhibit some of the most remarkable phenonomena found in condensed matter systems. They typically involve many active degrees of freedom (spin, charge, orbital), which leads to numerous competing states and complicated phase diagrams. A new perspective on correlated many-body systems is provided by the nonequilibrium dynamics, which is being explored in transport studies on nanostructures, pump-probe experiments on correlated solids, and in quench experiments on ultra-cold atomic gases.An advanced theoretical framework for the study of correlated lattice models, which can be adapted to nonequilibrium situations, is dynamical mean field theory (DMFT). One aim of this proposal is to develop ""nonequilibrium DMFT"" into a powerful tool for the simulation of excitation and relaxation processes in interacting many-body systems. The big challenge in these simulations is the calculation of the real-time evolution of a quantum impurity model. Recently developed real-time impurity solvers have, however, opened the door to a wide range of applications. We will improve the efficiency and flexibility of these methods and develop complementary approaches, which will extend the accessible parameter regimes. This machinery will be used to study correlated lattice models under nonequilibrium conditions. The ultimate goal is to explore and qualitatively understand the nonequilibrium properties of ""real"" materials with active spin, charge, orbital and lattice degrees of freedom.The ability to simulate the real-time dynamics of correlated many-body systems will be crucial for the interpretation of experiments and the discovery of correlation effects which manifest themselves only in the form of transient states. A proper understanding of the most basic nonequilibrium phenomena in correlated solids will help guide future experiments and hopefully lead to new technological applications such as ultra-fast switches or storage devices."