Answer:
Before the Umayyads, Islamic rule was non-centralized. The military was organized under the caliphate, a political structure led by a Muslim steward known as a caliph, who was regarded as the religious and political successor to the prophet Muhammad. The early caliphate had a strong army and built garrison towns, but it did not build sophisticated administrations. The caliphate mostly kept existing governments and cultures intact and administered through governors and financial officers in order to collect taxes.
The Rashidun caliphate was also not dynastic, meaning that political leadership was not transferred through hereditary lineage.^11start superscript, 1, end superscript During this period, it seems the Arab tribes retained their communal clan-based systems of choosing leaders.
However, to sustain such a massive empire, more robust state structures were necessary, and the Umayyads began developing these structures, which were often influenced by the political structures in neighboring empires like the Byzantines and Sasanians. Under the Umayyads, a dynastic and centralized Islamic political state emerged.
The Umayyads shifted the capital from Mecca to Syria and replaced tribal traditions with an imperial government controlled by a monarch. They replaced Greek, Persian, and Coptic with Arabic as the main administrative language and reinforced an Arab Islamic identity. Notably, an Arab hierarchy emerged, in which non-Arabs were accorded secondary status. The Umayyads also minted Islamic coins and developed a more sophisticated bureaucracy, in which governors named viziers oversaw smaller political units.
The Umayyads did not actively encourage conversion, and most subjects remained non-Muslim. Because non-Muslim subjects were required to pay a special tax, the Umayyads were able to subsidize their political expansion.

A map depicting the extent of the Umayyad caliphate in 750 CE, which extended from Spain in the west to northern India in the East and covered northern Africa, southern Europe, Anatolia, and the Arabian Peninsula.
This map shows the extent of the Umayyad Empire in 750 CE. Image credit: Wikipedia.
The Umayyads did not come into power smoothly. The transition between the rule of the Rashidun and the first Umayyads was full of strife. Debates raged about the nature of Islamic leadership and religious authority. These conflicts evolved into major schisms between Sunni, Shia, and Ibadi Islam.
Ultimately, there were many factions that regarded the Umayyads as corrupt and illegitimate, some of whom rallied around new leaders. These new leaders claimed legitimacy through shared lineage with the prophet Muhammad, through the prophet’s uncle, Abbas. They led a revolt against the Umayyads, bringing the Abbasid caliphate to power.
The Abbasids were intent on differentiating themselves from their Umayyad predecessors, though they still had a lot in common. Abbasid leadership was also dynastic and centralized. However, they changed the social hierarchy by constructing a more inclusive government in a more cosmopolitan capital city, Baghdad. The distinction between Arab Muslims and non-Arab Muslims diminished, with Persian culture exerting a greater influence on the Abbasid court.

In the forefront, a decorated, gold structure. In the background, a tall minaret.
Dome of the Treasury, Umayyad Mosque, Damascus, Syria. The Dome was built in 789, while the mosque was completed in 715. Image credit: Wikipedia
Under the Abbasids, Islamic art and culture flourished. They are famous for inaugurating the Islamic golden age. Religious scholars, called ulema, developed more defined religious institutions and took on judicial duties and developed systems of law. It was also during Abbasid rule that many people converted to Islam, for a multitude of reasons including sincere belief and avoiding paying taxes levied on non-Muslims. As a result, Islamic culture spread over the Abbasids’ vast territory.