  Dispersive shock waves are fascinating phenomena occurring when nonlinearity
overwhelms linear effects, such as dispersion and diffraction. Many features of
shock waves are still under investigation, as the interplay with
noninstantaneity in temporal pulses transmission and nonlocality in spatial
beams propagation.
  Despite the rich and vast literature on nonlinear waves in optical Kerr
media, spatial dispersive shock waves in nonlocal materials deserve further
attention for their unconventional properties. Indeed, they have been
investigated in colloidal matter, chemical physics and biophotonics, for
sensing and control of extreme phenomena.
  Here we review the last developed theoretical models and recent optical
experiments on spatial dispersive shock waves in nonlocal media. Moreover, we
discuss observations in novel versatile materials relevant for soft matter and
biology.
