Nonlinear Waves in Lattices: Past, Present, Future

In the present work, we attempt a brief summary of various areas where non-linear waves have been emerging in the phenomenology of lattice dynamical systems. These areas include non-linear optics, atomic physics, mechanical systems, electrical lattices, non-linear 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.