Hulagu, the child of Tolui and a Christian woman, was dispatched by his brother Mongu Khan in 1255 to accomplish three tasks in southwest Asia. 1) the subjugation of the Lurs, a people of southern Iran 2) the destruction of the sect of the Assassins 3) the destruction of the Abbasid caliphate.
Hulagu marched out with perhaps the largest Mongol army ever assembled. Hulagu easily destroyed the Lurs, and his reputation so frightened the Assassins that they surrendered their impregnable fortress of Alamut to him without a fight.
Hulagu probably always intended to take Baghdad, but he used the caliph's refusal to send troops to him as a pretext for conquest. Hulagu sent a message to the caliph containing the following (trans. John Woods)
"When I lead my army against Baghdad in anger, whether you hide in heaven or in earth
I will bring you down from the spinning spheres; I will toss you in the air like a lion. I will leave no one alive in your realm; I will burn your city, your land, your self.
If you wish to spare yourself and your venerable family, give heed to my advice with the ear of intelligence. If you do not, you will see what God has willed."
The caliph was not sure what to do about Hulagu's invasion, but weakly defended the city. Hulagu ordered various sections of Baghdad's population spared, like learned men and Christians, but killed at least 250,000 people. (contemporary sources say 800,000). Hulagu killed the caliph by wrapping him in a rug and having him either "beaten to a pulp" or trampled by horses. Marco Polo reports that Hulagu starved the caliph to death, but there is no corroborating evidence for that.
Hulagu died in 1265. His undiscovered tomb is in Azerbaijan. The dynasty Hulagu established became known as the Il-Khans