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A major advance in density-matrix renormalization group (DMRG) calculationshas been achieved by the invention of highly efficient DMRG techniques for thesimulation of real-time dynamics of strongly correlated quantum systems in onedimension. Starting from established linear-response techniques in DMRG andearly attempts at real-time dynamics, we go on to review two current methodswhich both implement the idea of adapting the effective Hilbert space of DMRGto the quantum state evolving in time. We also give an outlook on extensions tofinite temperature calculations.

Methods for Time Dependence in DMRG