Pure magnesium (Mg) develops a strong basal texture after conventional processing of hot rolling or extrusion. Consequently, it exhibits anisotropic mechanical properties and is difficult to form at room temperature. Adding appropriate alloying elements can weaken the basal texture or even change it, but the improvement in formability and mechanical properties is still far from expectations. Over the past 20 years, considerable efforts have been made and significant progress has been made on wrought Mg alloys at the fundamental and technological levels. At the fundamental level, textures formed in sheets and extrusions of different alloy compositions and produced under different strain paths or thermomechanical processing conditions are relatively well established, with the assistance of the advanced characterization technique of electron backscatter diffraction. At the technological level, room temperature formability of sheet has been significantly improved, and tension-compression yield asymmetry of extrusion is also remarkably reduced or eliminated. This paper starts with an overview of dislocations, stacking faults and twins, and deformation of single crystals of pure Mg along different orientations and under different loading conditions, followed by a review of microstructure (texture and grain size) and deformation of polycrystalline pure Mg with different textures, grain sizes, and loading conditions. With this information as a base, texture, grain size, and deformation of polycrystalline Mg alloy sheets and extrusions produced under different processing conditions are systematically examined and compared. Remaining and emerging scientific and technology issues are then highlighted and discussed in the context of texture and grain size. The need for better-resolution diffraction and spectroscopy techniques is also discussed in the relationship between texture change and grain boundary solute segregation.