The influence of the Dzyaloshinskii-Moriya interaction (DMI) on the behavior of spin waves in ultra-thin ferromagnetic films and chiral magnonic crystals is reviewed [1]. 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 [2-3] and interfacial Dzyaloshinskii-Moriya coupling [4-6]. More recently, the concept of a chiral magnonic crystal has been introduced [7], where the interfacial Dzyaloshinskii-Moriya interaction is periodic. The effect of this periodicity includes additional features such as flat bands, indirect gaps, and an unusual spin-wave evolution, with standing waves showing finite phase velocities in the zones where the DMI is nonzero. These results have been obtained with micromagnetic simulations and using a theoretical approach based on the plane-wave method. These chiral magnonic crystals with periodic DMI, which may be attained for instance by covering a thin ferromagnetic film with an array of heavy-metal wires [7], host interesting physical properties, encouraging future experimental studies to prove and evidence these phenomena.