As a term, al-ḥākimiyyah was used for the first time by Abū Al-A‘la Al-Mawdūdī as he was seeking for the independence of his country from Britain. When Pakistan gained its independence and separated in 1947, Al-Mawdūdī abandoned the idea of al-ḥākimiyyah and subjected himself to state laws and constitution. Moreover, he ran for office.
Sayyid Quṭb developed this idea adding some extremist thoughts that Egypt is a Jāhilī state which lives in a state of disbelief because it does not judge in accordance with what Allah has revealed.
Since Sayyid Quṭb till this very day, terrorist groups use this term in order to rationalize their deviation from the straight path; they kill innocent people, destroy civilizations on the pretext that there is no rule except Allah's Rule and that Sharī‘ah shall be applied all over the world.