Reflecting new geopolitical and ethnic realities in the umma, the Abbasids moved the caliphal capital to Iraq, building Baghdad soon after. It was during the early to mid-Abbasid period (751-830) that the true flowering of Islamic civilization occurred encompassing law, theology, visual arts, and scientific enquiry. Also, while a modus vivendi was worked out with Byzantium involving yearly skirmishes and a mostly fixed border, in the West, an Ummayad Amir named Abd al-Rahman had escaped Abbasid massacre and crossed to Spain, founding the Ummayad Emirate of Spain from 756. This gave Iberian Islam political centralism for a while, though his descendents underwent political fragmentation.
Also at the end of the eighth century the Abbasids found they could no longer keep a huge polity larger than that of Rome together from Baghdad. In 793 the Shi'ite dynasty of Idrisids set up a state from Fez in Morocco, while a family of governors under the Abbasids became increasingly independent until they founded the Aghlabid Emirate from the 830s. By the 860s governors in Egypt set up their own Tulunid Emirate, so named for its founder Ahmad ibn Tulun. From this time Egypt would be ruled by dynasties separate from the Caliph. In the East as well, governors decreased their ties to the center. The Saffarids of Herat and the Samanids of Bukhara had broken away from the 870s, cultivating a much more Persianate culture and statecraft. By this time only the central lands of Mesopotamia were under direct Abbasid control, with Palestine and the Hijaz often managed by the Tulunids. Byzantium, for its part, had begun to push Arab Muslims farther east in Anatolia.
By the 920s, the situation had changed further. A Shi'ite sect only recognizing the first five Imams and tracing its roots to the Prophet's daughter Fatima took control of Idrisi and then Aghlabid domains. Called the Fatimid dynasty, they had advanced to Egypt in 969, establishing their capital near Fustat in Cairo, which they built as a bastion of Shi'ite learning and politics. By 1000 they had become the chief political and ideological challenge to Sunni Islam in the form of the Abbasids. By this time the latter state had fragmented into several governorships that, while recognizing caliphal authority from Baghdad, did mostly as they wanted, fighting with each other. The Caliph himself was under 'protection' of the Buyid Emirs who possessed all of Iraq and western Iran, and were quietly Shi'ite in their sympathies. To the East was the first major Turkish Islamic state, the Ghaznavids under Mahmud.
In the Islamic West, after generations of political infighting among rival Islamic Amirs, the Ummayad Abd al-Rahman III was able to establish himself a Caliph of a united polity. Centered on Cordoba and Toledo, he and his vizir al-Mansur raided both the Shi'ite Fatimids as well as the Christian neighbors at Barcelona, Burgos, Leon, and Santiago de Compostela. As for the Christian states on the peninsula, from the 730s, the tiny Kingdom of Asturias, centered on Oviedo in northern Spain, had soldiered on, exposed to continuous Muslim raiding. This was in addition to Charlemagne's March in Catalonia on the Pyrenees. In the early 900s, the Asturias king took advantage of Muslim infighting to move his capital south to Leon and the County of Castile. Though not a Crusader-type state and content to work with Muslim amirs in order to survive, its leaders began to attract freemen as colonists with generous offers of agricultural land and tax rebates. Warring with Muslims when it suited them, Castilian leaders were not at this point fighting a holy war. For their part, Abd al-Rahman's forces raided Pamplona, but did not prevent slow advances out of the Pyrenees, based on fortress building and conquest of Christian held points. Good relations with al-Mansur were maintained. By 1034, Sancho the Great had incorporated Aragon, Sobrarbe, Barcelona, as well as Asturian Leon and Castile.
The Islamic polity of the 700s, which had encapsulated the majority of the known world of Antiquity in lightning speed, had its roots in pagan Arab tribesmen mired in clannish warfare, and mostly illiterate. The obvious question is how they were able to conquer the Sassanians, route the Byzantines, and establish a state from Spain to India. Before moving to internal issues, let us consider the environment. The two states against which early Islam abutted were Byzantium and Sassanian Persia. As regards the latter, in the 630s, it was in the midst of coups a the political center occasioned by the momentous loss to Byzantium under Heraclius. As well, none of its border defenses had been resurrected since the conflict, and its army size was much reduced. Client tribes in northern Arabia, the Lakhmids, were only nominally loyal, and had used the war years to drift away from Persian control. Thus, the Arabs were facing a northeastern enemy that was much enervated, and not able to attract the emotional loyalty of a mostly non-Zoroastiran population in areas of initial Sassanian-Islamic conflict. Byzantium's condition was not dissimilar. It too had not had time to restore defenses in those areas from with the Persian had withdrawn only recently, such as the Levant and Egypt. It too, had suffered tremendous human and material losses. Further, its client Arabian tribes, the Ghassanids, had also drifted away when not paid. More unique to Byzantium, however, was the religious issue. Though the Levant and Egypt were solidly Christian, its population's majority was not Orthodox. Monophysitism was dominant in Egypt and parts of Palestine, while Nestorianism was widespread in Syria and Mesopotamia. As emperors and the Constantinople church had gone back and forth on the issue, ultimately condemning and proscribing both approaches, Byzantine administration had gone a long way to alienating large segments of the population in those very areas Muslims were to conquer with their offers of religious toleration in return for political control. This was also true for the Jewish communities scattered throughout the region. Thus, there was very little reason for many to defend Byzantium in the Middle East. Finally, one cannot avoid the sense that after forty years of internal political unrest combined with exhausting Persian wars and Avar incursions, Byzantine state, society, and military exhibited a sense of fatigue and inability to assimilate the crisis' meaning so soon after the Sassanian conflict. Of course, the element of chance--a dust storm blinding Byzantine troops near the Yarmuk--cannot be discounted.
Turning to factors internal to the Muslims, the most mundane are nonetheless important. The Islamic umma was something with which tribal Arabs could identify. A super-tribe based on allegiance to a leader who had demonstrated increasing success at beating opponents, the prospect of raiding on a wider scale after 634 would be lucrative and quite attractive to them. Often tribes as a whole came into the new religion, and were deployed and settled as such. Beyond that, Arab fighters, on foot and horseback, were light and mobile, much more so than their Byzantine or Persian counterparts. Not having population centers and always on the move, it was impossible for Byzantine forces in particular to draw them into the kind of combat conducive to victory. In such a situation, raiding success bred enthusiasm for continual conquest, with over-extension not a danger.