What was the relationship between Genghis Khan and Kublai Khan?

Kublai Khan was the fourth son of Tolui and a grandson of Genghis Khan.

Genghis Khan (birth name Temujin) was born around 1162 in present day Mongolia, the son of a Mongol chieftain, united the different tribes north of the Gobi Desert and launched a series of campaigns to conquer a large portion of Eurasia. By the time of his death in 1227, Mongol armies had fought and toppled kingdoms and empires from Korea to the Caspian Sea.

Kublai Khan, born in 1215, did not possess the same interest in nomadic life, but was drawn to Chinese culture, after his older brother, Mongke died, Kublai became the Great Khan, but had to fight his younger brother in order to solidify his power. Kublai accomplished what his grandfather had attempted, conquest all of China. Genghis Khan had conquered the northern Jin dynasty, but the southern Song dynasty remained. Kublai completed the conquest and became the first non-native to conquer and rule over China. His ascension to Great Khan marked the final division of the empire into 4 distinct regions, China and Mongolia (Yuan Dynasty founded by Kublai), Persia (Ilkhanate), the Russian steppes (Golden Horde) and central Asia (Chagatai Khanate). Kublai would be the last Great Khan to attempt to hold power over the other khanates.