  In the present work, we attempt a brief summary of various areas where
nonlinear waves have been emerging in the phenomenology of lattice dynamical
systems. These areas include nonlinear optics, atomic physics, mechanical
systems, electrical lattices, nonlinear metamaterials, plasma dynamics and
granular crystals. We give some of the recent developments in each one of these
areas and speculate on some of the potentially interesting directions for
future study.
