Historically, the Khawaarij are those who rebelled against ‘Ali ibn Abee Taalib (رضي االله عنه) in the 37th year of Hijrah (657 C.E.) and imputed kufr upon ‘Ali (رضي االله عنه) upon the arbitration that followed the Battle of Siffeen. They hated ‘Ali’s decision to end the fitnah which occurred with Mu’aawiyah (رضي االله عنه), calling ‘Ali’s acceptance of the arbitration a compromise. They also imputed kufr upon many of the sahaabah who accepted the arbitration. They did not even accept the whole of ‘Uthman’s (رضي االله عنه) Caliphate. This position stems from their misunderstanding of the Qur’aan. They deduced, wrongly, that major sins are kufr and thus forfeit salvation. Sin is a contradiction that nullifies faith! ‘Ali and the other sahaabah sinned in the eyes of the Khawaarij and that sufficed to nullify their state of belief! Their doctrine became famous in their rebellions against any Muslim leader who, in their eyes, committed a sin or a mistake.
The Prophet (صَلَّى اللّٰهُ عَلَيْهِ وَسَلَّم) informed us before his death of the emergence of this sect and that,
“They will kill the Muslims and leave the idolaters. Should I live until they appear, I would kill them as the killing of the nation of ‘Aad.”
He (صَلَّى اللّٰهُ عَلَيْهِ وَسَلَّم) also said:
“The Khawaarij are the dogs of the Fire.”
‘Ali (رضي االله عنه) delegated ibn ‘Abbaas ( رضي االله عنهما) to call them to the truth. He succeeded in convincing several thousands of them. Those who rejected continued to spread mischief even after ‘Ali (رضي االله عنه) warned them against it. He finally fought them in the battle of an-Nahrawaan (38Hj/658) and only few of them escaped and continued the secession. ‘Ali (رضي االله عنه) was himself killed by a Kharijite by the name of Ibn Muljam. They split into many groups and today they survive in ‘Oman, Tunisia, Libya, Algeria, and in Tanzania and they are known as the Ibaadiyyah (ibadi Kharijism).
The Khawaarij sect was later influenced by scholastic theology and its principles became very close to those of the Jahmite and Mu’tazilite sects. They center upon the following matters:
(1) Imputing kufr upon ‘Ali, ‘Uthmaan and other sahaabah (رضي االله عنهم أجمعين)
(2) The right to rebel and fight the Muslim rulers who may err or sin.
(3) Justifying the rebellion and fight against disobedient Muslims (rulers and/or ruled) and that it is permissible for them to secede from the general body of the Muslims.
(4) They believe that the Qur’aan is created.
However, the Qur’aan is the literal Word of Allaah Who uttered it in letter and sound and which He Spoke to Jibreel (alaihissalam), directly without a mediator, and who then brought it down to the Prophet Muhammad (صَلَّى اللّٰهُ عَلَيْهِ وَسَلَّم). The Qur’aan is neither the word of Jib reel nor the word of Prophet Muhammad (صَلَّى اللّٰهُ عَلَيْهِ وَسَلَّم).
(5) They distort the meanings of Allaah’s Attributes by resorting to figurative interpretation.
(6) Like the twelver Shee’ites and other deviant sects, they deny that the believers will see Allaah on the Day of Resurrection. This contradicts what is asserted in the Qur’aan and authentic sunnah.
(7) Imputing kufr on the Muslims who commit major sins.
(8) The majority of the Khawaarij deny the actual punishment in the grave that Allaah (سبحانه و تعالى ) inflicts upon those who deserve it.
The aforementioned are some of the major characteristics of the Khawaarij. I intended to give the reader some background about this very dangerous sect and which has influenced many Muslim groups and parties in our times leading to bloodshed in many parts of the Muslim World. The bloody confrontations are hard to stop in some places and that has distorted the view of Islam in many parts of the world.
The truth, however, is emerging and will inshaa’ Allaah completely emerge on the hands of the true followers of Islam who are working hard to correct this problem with the good word without compromising the ‘aqeedah nor the manhaj.
We should be able to present the truth without imitating the kuffaar and their ways. In this respect, the words of Imaam Maalik (رحمه االله) are remembered:
“Nothing will benefit this ummah to come except that which benefited its early generations.” 
This refers to the correct creed, methodology and righteous deeds.
Another point of benefit is that the Muslim should be aware that the principles of many of these sects are still alive and propagated by certain individuals and/or groups, and accordingly the believer must be cautious. 
 An agreed upon hadeeth [i.e. reported by al-Bukhaari and Muslim]. [See Saheeh alBukhaari (Arabic/English)], vol. 9, no. 527.
 Reported by Ahmad, Ibn Maajah, Ibn Abee ‘Aaasim, and others. Shaykh al-Albaani authenticated the isnaad of the narration reported by Ibn Maajah and Ibn Abee ‘Aasim. He also said that the isnnad of Ahmad’s report is hasan. [See As-Sunnah by Ibn Abee ‘Aasim, no. 904, and 905], p. 424.
 Related by Imaam Ibn ‘Abdil-Barr in At-Tamheed (23:1).
 See Fathul-Baari by al-Haafith Ibn Hajar, vol. 12, pp. 282-284, 287,289 and Wasatiyyat Ahlus-Sunnah Baynal Firaq (“The Distinguished Medium Path of AhlusSunnah vis-à-vis the Sects), by Dr. Muhammad ba-Kareem ba-‘Abdullaah [Riyadh, Saudi Arabia: Daarur-Raayah, 1415/1994,], pp. 290-291.
Source : Appendix B from the eBook: Tafseer Ayatul-Kursi. Prepared by Dr. Saleh As-Saleh (rahimahullah)