  The influence of the Dzyaloshinskii-Moriya interaction in ultra-thin
ferromagnetic films and chiral magnonic crystals on the behavior of spin waves
is reviewed. During the last decade, it has been shown, both theoretically and
experimentally, that this anisotropic exchange interaction produces
non-reciprocal features on the spin-wave spectrum of a magnetic system, a
phenomenon that occurs both for bulk and interfacial Dzyaloshinskii-Moriya
coupling. More recently, the concept of a chiral magnonic crystal has been
introduced, where the interfacial Dzyaloshinskii-Moriya interaction is
periodic. The effect of this periodicity include additional features such as
flat bands, indirect gaps, and an unusual spin-wave evolution.
