This is a review of the dynamics of wave propagation through a disordered
N-mode waveguide in the localized regime. The basic quantities considered are
the Wigner-Smith and single-mode delay times, plus the time-dependent power
spectrum of a reflected pulse. The long-time dynamics is dominated by resonant
transmission over length scales much larger than the localization length. The
corresponding distribution of the Wigner-Smith delay times is the Laguerre
ensemble of random-matrix theory. In the power spectrum the resonances show up
as a 1/t^2 tail after N^2 scattering times. In the distribution of single-mode
delay times the resonances introduce a dynamic coherent backscattering effect,
that provides a way to distinguish localization from absorption.Comment: 18 pages including 8 figures; minor correction
