Ali was Muhammad's cousin and son-in-law. He is the subject of lots of praises and devotional songs, especially by Shias and Sufis.
Narrated 'Ikrimah: That Ali burnt some people who apostasized from Islam. This news reached Ibn 'Abbas, so he (Ibn 'Abbas) said: "If it were me I would have killed them according to the statement of Messenger of Allah. The Messenger of Allah said: 'Whoever changes his religion then kill him.' And I would not have burned them because the Messenger of Allah said: 'Do not punish with the punishment of Allah.' So this reached 'Ali, and he said: "Ibn 'Abbas has told the truth." (Sahih)
It was narrated from Anas that: 'Ali came to some people of Az-Zutt, who worshipped idols, and burned them. Ibn 'Abbas said: "But the Messenger of Allah [SAW] said: 'Whoever changes his religion, kill him.'" (Sahih)
Beware! I called you (insistently) to fight these people night and day, secretly and openly and exhorted you to attack them before they attacked you, because by Allah, no people have been attacked in the hearts of their houses but they suffered disgrace; but you put it off to others and forsook it till destruction befell you and your cities were occupied.
Battle of Nahrawan
When Amir al-mu'minin showed his intention to fight the Kharijites, he was told that they had crossed the bridge of Nahrawan and gone over to the other side. Amir al-mu'minin said: "Their falling place is on this side of the river. By Allah, not even ten of them will survive while from your side not even ten will be killed."
Sahifa, Innovation, Curses
Ibrahim al-Taimi reported on the authority of his father: 'Ali b. Abu Talib (Allah be pleased with him) addressed us and said: He who thinks that we (the members of the Prophet's family) read anything else besides the Book of Allah and this Sahifa (and he said that Sahifa was tied to the scabbard of the sword) tells a lie. (This Sahifa) contains (problems) pertaining to the ages of the camels and (the recompense) of the injuries, and it also records the words of the Prophet (ﷺ): Medina is a sacred territory from 'Ayr to Thaur (it is most probably Uhud). He who innovates (an act or practice) or gives protection to an innovator, there is a curse of Allah and that of His angels and that of the whole humanity upon him. Allah will not accdpt from him (as a recompense) any obligatory act or supererogatory act, and the responsibility of the Muslims is a joint responsibility; even the lowest in rank can undertake the responsibility (on behalf of others), and he who claims anyone else as his father besides his own father or makes one his ally other than the one (who freed him), there is a curse of Allah. that of His angels and that of the wholemankind upon him. Allah will not accept the obligatory act of the supererogatery act (as a recompense) from him.
Sahih Muslim 9:3601. See also