In the presentation I will show the results of investigation on spin waves in periodic ferromagnetic structures (magnonic crystals). The patterning at nanoscale permits to alter the propagation of spin waves and modify their properties. The focus of study is put on the following topics related to spin waves properties: i) standing spin wave formation in magnonic crystals ii) metamaterial properties for electromagnetic waves propagating through magnonic crystal, iii) nonreciprocal dispersion of spin waves and iv) collective dynamical skyrmion excitations in the arrays of magnetic dots.