  A major advance in density-matrix renormalization group (DMRG) calculations
has been achieved by the invention of highly efficient DMRG techniques for the
simulation of real-time dynamics of strongly correlated quantum systems in one
dimension. Starting from established linear-response techniques in DMRG and
early attempts at real-time dynamics, we go on to review two current methods
which both implement the idea of adapting the effective Hilbert space of DMRG
to the quantum state evolving in time. We also give an outlook on extensions to
finite temperature calculations.
