This PhD project focuses on the emerging phenomenon of spin wave non-reciprocity in cylindrical magnetic wires, from their fundamental properties, to their exploitation towards realizing magnonic diode based devices. Preliminary experiments conducted in our laboratory SPINTEC on cylindrical wires, with axial magnetization in the core and azimuthal magnetization on the wire surface, revealed a giant non-symmetrical effect (non-symmetrical dispersion curves with different speeds and periods for left- and right-propagating waves), up to an extent of creating a band gap for a given direction of motion, related to the circulation of magnetization (right or left). This particular situation has not been yet described theoretically or modeled, which sets an unexplored and promising ground for this PhD project. To model spin-wave propagation and derive dispersion curves for a given material we plan to use different numerical tools: our in-home 3D finite element micromagnetic software feeLLGood and open source 2D TetraX package dedicated to eigen modes spectra calculations. This work will be conducted in tight collaboration with experimentalists, with a view both to explain experimental results and to guide further experiments and research directions.