  All random wave fields possess a network of phase singularities. We show that
while the phase statistics within speckle patterns is generic, the statistics
of the motion of phase singularities differs substantially for diffusive and
localized waves. This reflects the changing wave interaction with the
underlying modes of multiply-scattering systems. Universality is regained when
the motion of phase singularities is charted against the phase excursion which
reflects the variation of phase change across the speckle pattern. The
evolution of speckle patterns can therefore be used to monitor internal motion
in complex systems and to characterize the nature of wave propagation.
