The Abbasids came to power in 750 on a movement that promised rule by the Prophet's family and delivered rule by his uncle's descendants. They moved the centre of the Islamic world from Syria to Iraq, founding Baghdad in 762 as a round city on the Tigris, and adopted a court style, drawn substantially from Sasanian precedent, in which the caliph was styled the shadow of God on earth and sat behind a curtain.
Their most durable achievement was intellectual. Across the eighth to tenth centuries a sustained, state-funded translation movement rendered Greek philosophy, medicine, mathematics and astronomy into Arabic, and the commentary and correction that followed made Baghdad the working centre of the sciences for three hundred years. The same period saw the four Sunni schools of law take shape, the great hadith collections compiled, and speculative theology established as a discipline.
Against that background the caliph al-Mamun in 833 imposed the mihna, a test requiring judges and scholars to affirm that the Quran was created rather than eternal. It was the one attempt by a caliph to define dogma, and it broke on the refusal of Ahmad ibn Hanbal, who was imprisoned and flogged and did not yield. Around 848 the policy was abandoned and reversed. The lesson was drawn permanently: doctrine belongs to the scholars, and the caliph enforces the law rather than making it.