The development of magnesium alloys, which exhibit high strength and high ductility (fracture toughness), is critical for ensuring the safety and reliability in structural applications. It is well-known that grain refinement and/or alloying are impressive strategies to attain such properties in metallic materials. In the former case, grain boundaries of magnesium and its alloys have unique characteristics, e.g., sites for non-basal dislocation activity and occurrence of partial grain boundary sliding. As a result, strength as well as ductility (fracture toughness) tend to increase and improve with grain refinement. In the latter case, 29 types of solid solution elements, which have a maximum solubility of more than 0.1 at%, can dissolve in magnesium. Several elements are generally added to magnesium simultaneously to achieve good mechanical properties via a synergistic effect. In industrial fields, ternary magnesium alloys such as Mg–Al–Zn and Mg–Zn–Zr alloys, which have fine-grained structures, have been widely used; however, there is no still clear and systematic understanding of the impact of various alloying elements on properties for magnesium. In this paper, we review recent studies on the effect of solid solution alloying elements on ductility (fracture toughness), with focusing on polycrystalline binary magnesium alloys. With regard to the toughness, the crack-propagation behavior and/or fracture behavior are quite sensitive to the alloying element, regardless of grain size. Twin boundaries in particular are recognized as harmful defects, because they act as crack-propagation sites. Nevertheless, changing the electric bonding behavior through alloying has the potential to increase the toughness. As for the ductility, the alloying elements also dramatically affect the room-temperature plastic deformation. In addition to the activation of the non-basal dislocation slip, grain boundary sliding also plays a notable role in enhancing the elongation-to-failure in tension. This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 83 (2019) 65–75.