Strong quantum correlations which are at the heart of many quantum phenomena of current interest such as low-dimensional magnetism or high-temperature superconductivity imply that no easy identification of relevant states in the Hilbert space is possible. Over the years, highly successful analytical and numerical techniques to study the static and dynamic properties of such systems at or very close to equilibrium have been developed. However, in recent years, the even more complicated real-time evolution of such quantum systems far from equilibrium has become the focus of interest, such as in the time-dependent quantum phase transitions in ultracold atom gases in optical lattices or in charge and magnetization transport in quasi-one dimensional strongly correlated structures. Recently, it has been possible, using concepts from quantum information theory, to extend one of the standard tools of numerical simulation, the density matrix renormalization group (DMRG), to simulate time evolutions of low-dimensional strongly correlated quantum systems over long times at almost the precision obtained for static properties. I want to outline the conceptual progress made, and demonstrate the versatility of the method in various fields of applications.