  This article provides a detailed review on the generalized dynamics of
soft-matter quasicrystals developed recent years. Comparing to solid
quasicrystals consisted mainly with metallic alloys, soft-matter quasicrystals
have been observed in liquid crystals, polymers, colloids, nanoparticles, and
surfactants, which indicate quite different formation mechanism. Based on
Landau-Anderson theory and group representation theory, we have studied the
symmetry, symmetry breaking and elementary excitations for the observed and
possible soft-matter quasicrystals. We further proposed one more elementary
excitation: fluid phonon additional to the phonon and phason for solid
quasicrystals, to quantitatively describe the dynamics of soft-matter
quasicrystals. The general governing equations and the solutions of the
dynamics evolution on the distribution, deformation and motion of the new phase
are studied, which reveal quite distinguishing dynamic behavior with those of
conventional fluids and solid quasicrystals. Some applications are introduced,
which show this is an important field of new materials and materials science.
