Who completed the conquest of the song?

The conquest of the Song Dynasty was completed by the Mongol Empire under Kublai Khan, the grandson of Genghis Khan. This culminated in 1279 with the fall of the Song capital, Hangzhou, after prolonged military campaigns that began in the 1230s. Kublai Khan established the Yuan Dynasty, marking the first time in history that the entire territory of China was under foreign rule.