Abu Bakr ʿAbd al-Karīm ibn al-Faḍl, better known by his regnal name al-Ṭāʾiʿ liʾllāh/biʾllāh, was the Abbasid caliph of Baghdad from 974 to his deposition in 991. He was in office during the domination of Iraq by the Shi'a Buyid dynasty, and as a result is generally considered a powerless figurehead under the thumb of the Buyid emirs. His tenure was also marked by strife between rival Buyid rulers and the frequent change of hands of Baghdad: al-Ta'i' himself was raised to the throne by a rebel Turkic general, Sabuktakin, who deposed al-Ta'i's father, al-Muti'. During periods of such strife, al-Ta'i' was able to exert some measure of political independence, but under stronger rulers he was sidelined, and was obliged to marry the daughters of the emirs Izz al-Dawla and Adud al-Dawla. Al-Ta'i's status suffered under Adud al-Dawla in particular, who turned to pre-Islamic Persian models for legitimacy, and relegated Iraq to the status of a simple province ruled from Fars. Al-Ta'i' was deposed on 22 November 991 by Baha al-Dawla, and replaced with his cousin, al-Qadir. He spent the rest of his days, until his death in 1003, confined to the caliphal palace.

Abū ʾl-Qāsim al-Faḍl ibn al-Muqtadir, better known by his regnal name of al-Mutīʿ li-ʾllāh, was the Abbasid caliph in Baghdad from 946 to 974, ruling under the tutelage of the Buyid emirs.