The formation of deformation-induced shear bands plays an important role for the room temperature deformation of both, Mg and Mg-Y alloys, but the formation and structure of shear bands is distinctively different in the two materials. Due to limited deformation modes in pure Mg, the strain is localized in few shear bands leading to an early failure of the material during cold deformation. Contrarily, Mg-RE (RE: rare earth) alloys exhibit a high density of homogeneously distributed local shear bands during deformation at room temperature. A study of the microstructure of the shear bands by electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) at different strains was performed. These investigations give insight into the formation of shear bands and their effects on the mechanical behaviour of pure Mg and Mg-3Y. Since in pure Mg mainly extension twinning and basal <a> dislocation slip are active, high stress fields at grain resp. twin boundaries in shear bands effect fast growth of the shear bands. In Mg-RE alloys additionally contraction and secondary twinning and pyramidal <c+a> dislocation slip are active leading to the formation of microscopic shear bands which are limited to the boundary between two grains. The effects of shear bands on the mechanical behaviour of pure Mg and Mg-RE alloys are discussed with respect to their formation and growth.