Mongol conquest of the Song dynasty

The Mongol conquest of the Song dynasty under Kublai Khan (r. 1260–1294) was the final step for the Mongols to rule the whole of China. It is also considered the Mongol Empire's last great military achievement.
Background
Before the Mongol–Jin War escalated, an envoy from Song China arrived at the court of the Mongols, perhaps to negotiate a united offensive against the Jin dynasty, who the Song had previously fought during the Jin–Song Wars. Although Genghis Khan refused, on his death in 1227 he bequeathed a plan to attack the Jin capital by passing through Song territory. Subsequently, a Mongol ambassador was killed by the Song governor in uncertain circumstances. Before receiving any explanation, the Mongols marched through Song territory to enter the Jin's redoubt in Henan. In 1233 the Song dynasty finally became an ally of the Mongols, who agreed to share territories south of the Yellow River with the Song. Song general Meng Gong defeated the Jin...