  Disordered hyperuniform structures are an exotic state of matter having
suppressed density fluctuations at large length-scale similar to perfect
crystals and quasicrystals but without any long range orientational order. In
the past decade, an increasing number of non-equilibrium systems were found to
have dynamic hyperuniform states, which have emerged as a new research
direction coupling both non-equilibrium physics and hyperuniformity. Here we
review the recent progress in understanding dynamic hyperuniform states found
in various non-equilibrium systems, including the critical hyperuniformity in
absorbing phase transitions, non-equilibrium hyperuniform fluids and the
hyperuniform structures in phase separating systems via spinodal decomposition.
