The first great Muslim state, the Umayyad Caliphate, lasted from 661 to 750, and their conquests stretched from Pakistan to Spain. In 747 the Abbasids, a family claiming descent from Abbas, an uncle of the Prophet Muhammad, began a revolt in Persia, and by 750 they were masters of the entire Islamic world, except for Spain, which the defeated Umayyads hung on to.

Their empire began to break up in 793, when a Shiite dynasty called the Idrisids declared a caliphate at their newly-founded city of Fez in Morocco. This was the first major Shiite challenge to Sunni dominance. The Aghlabid emir of Tunisia, nominally an Abbasid vassal, drifted out of their power. Then Egypt, Syria, and Arabia were taken over by a Tulunid dynasty founded in 868, and Persia split up into several emirates that refused to recognize Abbasid temporal power, so that by this time the Abbasids ruled little more than Mesopotamia.

The Abbasids recovered in 900 by retaking Persia, and defeating the Tulunids in 905, but their next major rival was now forming in the west, where a Shiite Fatimid dynasty had overcome the Idrisids and Aghlabids and was trying to move against Egypt. They were Arabs with a powerful base of Berber followers. They succeeded in 969, founding the city of Cairo as their new capital, and moved on to take Syria and Mecca. With the collapse of their power base the Abbasid caliphs lost all their temporal rule.

There was a brief resurgence of Abbasid power in the twelfth century. In 1055 the Seljuks, a Turkish tribe, had deprived the Fatimid rulers of Egypt of their Asian territories, Syria and Arabia, and when the Seljuks themselves were weakened and smaller states sprang up, the Abbasid caliphs resumed power over southern Mesopotamia. This period came to an end with the Mongol sack of Baghdad in 1258 under their Ilkhan Hulegu.

The Abbasid rulers are generally known by a laqab or honorific title, which is why they all begin with al- 'the': they called themselves things like 'the Righteous'. Relationship of rulers is son of preceding if not otherwise indicated.

Abu al-Abbas as-Saffah 750-754
al-Mansur              754-775  (br.)
al-Mahdi               775-785
al-Hadi                785-786
Harun al-Rashid        786-809  (br.)
al-Amin                809-813
al-Mamun               813-833  (br.)
al-Mutasim             833-842  (br.)
al-Wathiq              842-847
al-Mutawakkil          847-861  (br.)
al-Muntasir            861-862
al-Mustain             862-866  (gr. of al-Mutasim; deposed)
al-Mutazz              866-869  (s. of al-Mutawakkil)
al-Muhtadi             869-870  (s. of al-Wathiq)
al-Mutamid             870-892  (s. of al-Mutawakkil)
al-Mutadid             892-902  (nephew)
al-Muktafi             902-908
al-Muqtadir            908-932  (br.)
al-Qahir               932-934  (br.; deposed)
ar-Radi                934-940  (s. of al-Muqtadir)
al-Muttaqi             940-944  (br.; deposed)
al-Mustakfi            940-946  (s. of al-Muktafi; deposed)
al-Muti                946-974  (s. of al-Muqtadir; deposed)
at-Tai                 974-991  (deposed)
al-Qadir               991-1031 (s. of al-Muttaqi)
al-Qaim               1031-1075
al-Muqtadi            1075-1094 (gr.)
al-Mustazhir          1094-1118
al-Mustarshid         1118-1135
ar-Rashid             1135-1136 (deposed)
al-Muqtafi            1136-1160 (s. of al-Mustazhir)
al-Mustanjid          1160-1170
al-Mustadi            1170-1180
an-Nasir              1180-1225
az-Zahir              1225-1226
al-Mustansir          1226-1242
al-Mustasim           1242-1258

Colin McEvedy, The New Penguin Encyclopedia of Medieval History
John Morby, The Wordsworth Handbook of Kings and Queens