Takfiri influenced by Qutbism
Sayyid Qutb
Sayyid Qutb could be said to have founded the actual movement of radical Islam. Unlike the other Islamic thinkers that have been mentioned above, Qutb was not an apologist. He was a prominent leader of the Muslim Brotherhood and a highly influential Islamist ideologue, and the first to articulate these anathemizing principles in his magnum opus Fī ẓilāl al-Qurʾān (In the shade of the Qurʾān) and his 1966 manifesto Maʿālim fīl-ṭarīq (Milestones), which lead to his execution by the Egyptian government. Other Salafi movements in the Middle East and North Africa and across the Muslim world adopted many of his Islamist principles. According to Qutb, the Muslim community has been extinct for several centuries and reverted to jahiliyah (the pre-Islamic age of ignorance) because those who call themselves Muslims have failed to follow the sharia law. In order to restore Islam, bring back its days of glory, and free the Muslims from the clasps of ignorance, Qutb proposed the shunning of modern society, establishing a vanguard modeled after the early Muslims, preaching, and bracing oneself for poverty or even death as preparation for jihad against what he perceived as jahili government/society, and overthrow them. Qutbism, the radical Islamist ideology derived from the ideas of Qutb, was denounced by many prominent Muslim scholars as well as other members of the Muslim Brotherhood, like Yusuf al-Qaradawi.Takfir in late 20th and early 21st century
Qutb and insurgents
By the mid 1990s, one list of Qutb-inspired groups included al-Jihaad al-Islami, Takfir wal-Hijra, Jund Allah, al-Jihaad, Tanzim al-Faniyyah al-Askariyyah—all of which were fighting violent insurgencies.While Qutb declared that the Islamic world had "long ago vanished from existence"  and that true Muslims would have to confront "arrogant, mischievous, criminal and degraded people" in the struggle to restore Islam, he had not specifically stated that the self-professed Muslim "authorities of the jahili system" were apostates (or whether they should all be killed)—but his followers have.
Ayman al-Zawahiri, "jihad's main ideologist," (originally of al-Jihaad al-Islami aka Egyptian Islamic Jihad), and the current leader of al-Qaeda, paid homage to Qutb in his book Knights under the Prophet's Banner Al Qaeda is commonly described as seeking to overthrow the "apostate" regimes in the Middle East and replace them with "true" Islamic governments, and having a "habit" of denouncing Muslims who did not "accept a narrow interpretation" of Sunni Islam as "non-believers and legitimate targets."Shukri Mustaf, founder  of Jama'at al-Muslimin (known to the public as Takfir wal-Hijra) had been in prison with Qutb, and was a "disciple" of his.The Takfir of Islamic State of Iraq and the Levant may be more rooted in Wahhabism and Ibn Abd al-Wahhab than Qutb,  but  "one famous quote" from him "has been seen written on walls and has also appeared repeatedly in IS texts: 'Whoever does not pay the price of jihad, shall pay the price of abstention'". Another source writes that the "roots" of ISIL's "takfiri" ideology "can be found in the Khawarij's view, and in the writings of Ibn Taymiyyah, Ibn Abd al-Wahhab, and Sayyid Qutb."