Kharijism

The Kharijites (, singular ) were an Islamic sect which emerged during the First Fitna (656–661). The first Kharijites were supporters of Ali who rebelled against his acceptance of arbitration talks to settle the conflict with his challenger, Mu'awiya, at the Battle of Siffin in 657. They asserted that "judgment belongs to God alone", which became their motto, and that rebels such as Mu'awiya had to be fought and overcome according to Qur'anic injunctions. Ali defeated the Kharijites at the Battle of Nahrawan in 658, but their insurrection continued. Ali was assassinated in 661 by a Kharijite

Ibadism (, ) is the third-largest branch of Islam. Its roots go back to the Kharijite secession from the fourth Caliph, Ali ibn Abi Talib. It is a moderate subsect that has persisted and led to the creation of Ibadi communities in various areas in the Middle East and Africa.

The Azariqa () were an extremist branch of the Kharijites who followed the leadership of Nafi ibn al-Azraq. Adherents of Azraqism participated in an armed struggle against the rulers of the Umayyad Caliphate, and they declared those who avoided this duty infidels - kafirs - and allowed their murder. Nafi ibn al-Azraq even permitted the killing of women and children of his opponents. At the same time, the Azraqites did not extend the principle of killing “apostates” to Christians and Jews, since they believed that they did not betray the teachings of the prophets Jesus and Moses.

The Najdat were the sub-sect of the Kharijite movement that followed Najda ibn 'Amir al-Hanafi, and in 682 launched a revolt against the Umayyad Caliphate in the historical provinces of Yamama and Bahrain, in central and eastern Arabia.

Muḥakkima (), also known as al-Haruriyya (), were the Muslims who rejected arbitration between Ali and Mu'awiya I at the Battle of Siffin in 657 CE. The name Muḥakkima derives from their slogan (), meaning "no judgment (hukm) except God's". The name al-Haruriyya refers to their withdrawal from Ali's army to the village of Harura' near Kufa. This episode marked the start of the Kharijite movement, and the term muḥakkima is often also applied by extension to later Kharijites.

Eighth century state in modern Algeria