Friction stir welding (FSW) is a promising approach for the joining of magnesium alloys. Although many Mg alloys have been successfully joined by FSW, it is far from industrial applications due to the texture variation and low mechanical properties. This short review deals with the fundamental understanding of weak zones from the viewpoint of texture analysis in FSW Mg alloys, especially for butt welding. Firstly, a brief review of the microstructure and mechanical properties of FSW Mg alloys is presented. Secondly, microstructure and texture evolutions in weak zones are analyzed and discussed based on electron backscatter diffraction data and Schmid factors. Then, how to change the texture and strengthen the weak zones is also presented. Finally, the review concludes with some future challenges and research directions related to the texture in FSW Mg alloys. The purpose of the paper is to provide a basic understanding on the location of weak zones as well as the weak factors related to texture to improve the mechanical properties and promote the industrial applications of FSW Mg alloys.