The Mongols swept into [Baghdad] on February 13 [1257] and began a week of massacre, looting, rape, and destruction.
As far as damage done, the sack of Baghdad by the Mongols made the sack of Rome by Alaric look kindly. The Grand Library of Baghdad, containing countless precious historical documents and books on subjects ranging from medicine to astronomy, was destroyed. Survivors said that the waters of the Tigris ran black with ink from the enormous quantities of books flung into the river. Citizens attempted to flee, but were intercepted by Mongol soldiers who raped and killed with abandon.
Although death counts vary widely and cannot be easily substantiated, a number of estimates do exist. Martin Sicker writes that close to 90,000 people may have died (Sicker 2000, p. 111). Other estimates go much higher. Muslim historian Abdullah Wassaf claims the loss of life was several hundred thousand or more. Ian Frazier of The New Yorker says estimates of the death toll have ranged from 200,000 to a million.
The Mongols looted and then destroyed. Mosques, palaces, libraries, hospitals — grand buildings that had been the work of generations were burned to the ground. ... Prior to this, the Mongols destroyed a city only if it had resisted them. Cities that capitulated at the first demand for surrender could usually expect to be spared. Cities that surrendered after a short fight, such as this, normally could expect a sack, but not complete devastation. The utter ferocity of the rape of Baghdad is the worst example of Mongol excess known. ...[From the article "once the takeover ended, the bloodshed ended." -- probably because there was no one left to kill! The Mongols "exercised a genius for speaking to people in terms that they understood." Everybody understands "Submit or die!"]
Baghdad was a depopulated, ruined city for several centuries... Of all the Mongol Khans, [Hulagu] is, for obvious reasons, the most feared and despised.
Aftermath
Thus was the caliphate destroyed, and Mesopotamia ravaged — it has never again been such a major center of culture and influence. ...[due to a succession crisis] after 1258 there was no unified Mongol Empire, but four separate kingdoms, including the Il-Khanate of Persia established by Hulagu. [The world conquered by the Mongols was a good deal smaller than the real one, and their unified rule extremely brief in historical terms.]
In the meantime, the Mongols led by Kitbuqa had fallen out with the crusaders holding the coast of Palestine, and the Mamluks were able to ally with them [the crusaders, that is], pass through their territory, and destroy the Mongol army at the Battle of Ain Jalut. {This was the first significant defeat of Mongol armies and ensured the security of Egypt from the Mongols.} Palestine and Syria were permanently lost, the border remaining the Tigris for the duration of Hulagu's dynasty.
[After the succession crisis was resolved in Mongolia] Hulagu returned to his [newly conquered] lands [near Iraq] by 1262, but instead of being able to avenge his defeats, was drawn into civil war with Batu Khan's brother Berke.

Iraq enjoyed a century of peace and a renaissance that brought the region to a level of prosperity and cultural sophistication higher than it enjoyed before or after.