Sorghaghtani Beki in the context of "Keraite"

Hulegu Khan, also known as Hülegü or Hulagu (c. 1217 – 8 February 1265), was a Mongol ruler who conquered much of Western Asia. As a son of Tolui and the Keraite princess Sorghaghtani Beki, he was a grandson of Genghis Khan and brother of Ariq Böke, Möngke Khan, and Kublai Khan.

Hulegu's army greatly expanded the southwestern portion of the Mongol Empire, founding the Ilkhanate in Persia. Under Hulegu's leadership, the Mongols sacked and destroyed Baghdad, ending the Islamic Golden Age and the Abbasid dynasty. They also weakened Damascus, causing a shift of Islamic influence to the Mamluk Sultanate in Cairo.

Kublai Khan (23 September 1215 – 18 February 1294), also known by his temple name as the Emperor Shizu of Yuan and his regnal name Setsen Khan, was the founder and first emperor of the Mongol-led Yuan dynasty of China. He proclaimed the dynastic name "Great Yuan" in 1271, and ruled Yuan China until his death in 1294.

Kublai was the second son of Tolui by his chief wife Sorghaghtani Beki, and a grandson of Genghis Khan. He was almost 12 when Genghis Khan died in 1227. He had succeeded his older brother Möngke as Khagan in 1260, but had to defeat his younger brother Ariq Böke in the Toluid Civil War lasting until 1264. This episode marked the beginning of the division of the Mongol Empire. Kublai's real power was limited to the Yuan Empire, even though as Khagan he still influenced the Ilkhanate and, to a significantly lesser degree, the Golden Horde.

Tolui (c. 1191 – 1232) was the youngest son of Genghis Khan and Börte. A prominent general during the early Mongol conquests, Tolui was a leading candidate to succeed his father after his death in 1227 and ultimately served as regent of the Mongol Empire until the accession of his brother Ögedei two years later. Tolui's wife was Sorghaghtani Beki; their sons included Möngke and Kublai, the fourth and fifth khans of the empire, and Hulagu, the founder of the Ilkhanate.

Tolui was less active than his elder brothers Jochi, Chagatai, and Ögedei during their father's rise to power, but once he reached adulthood he was considered the finest warrior of the four. He commanded armies under his father during the first invasion of Jin China (1211–1215), and his distinguished service during the Mongol invasion of the Khwarazmian Empire secured his reputation. After the fall of the cities of Transoxiana in 1220, Genghis dispatched Tolui early the following year to subjugate the region of Khorasan, which had begun to cause trouble for the Mongol armies. Tolui executed his orders with ruthless efficiency, assaulting the major cities of Merv, Nishapur, and Herat, and subjugating numerous others. Medieval chroniclers attributed more than three million deaths to the massacres he ordered at Nishapur and Merv; while these figures are considered exaggerated by modern historians, they are evidence of the abnormal brutality of Tolui's campaign.