Damascus under the Ommeyades became one of the most beautiful cities of the world and the metropolis of the Islamic Empire. Upon the abdication of Hassan, Muawiyah became the fact ruler of the Islamic Empire. The seat of government which Ali had fixed at Kufa was now removed to Damascus where Muawiyah surrounded himself with the pomp and pageantry of the Persian and Byzantine monarchs. Muawiyah was astute, unscrupulous, clear-headed, and pitiless. He was the founder of the Ommeyades Dynasty and applied himself with assiduity to the good government of the Empire. His rule was prosperous and peaceful at home and successful abroad. The Ommeyades were thoroughly touched by the magnificent churches and the dainty places in the Byzantine cities. Therefore, they imitated this architecture modifying it. Later, they adopted the Islamic art with its own particular style which can be seen in the Great Mosque in Damascus. Their fine taste can be seen in architecture, drawings and ornaments. And generally speaking, the Islamic Empire reached its zenith in the time of the Ommeyades.
Under the Republic, the Caliph was elected by the entire the entire population of El Medina. From Muawiyah's time, the reigning caliph nominated his successor, and the grandees and military chiefs took the covenant in the royal presence. While in the provinces, the oath was taken by the government on behalf of the presumptive caliph. Once the oath was taken, the suffrage of the people (obtained whether by coercion cajolery or bribe) was supposed to give a sacramental character to the election.
In the reign of Muawiyah Ibn Abu Sufian, Sind and the lower valley of the Indus were conquered by Muhallib Ibn Abu Sufra. Eastern Afghanistan was also brought under subjection about the same time. Soon after the accession of Al-Walid Ibn Abdul Malik, Kotaiba was appointed lieutenant. The Sogdians (who inhabited the countries in Central Asia to the north of the River Oxus) rose against the Arabs, expelled the residents and killed the colonists. After ten year of incessant warfare, kotaiba subjugated the whole of Central Asia to the confines of kashgar. About the same time, Mohamed Ibn Qasim led an expedition into India which ended in the annexation of Sind, Multan and a part of Punjab.
Muawiyah turned his attention to the invasion of Africa which had first taken place in the reign Omar. Under Omar, the Arab forces had advanced as far as Barca and the Romans undertook to pay an annual tribute to the Arabs who then withdrew from the country leaving small garrisons at Zawilah and Barca. The roman governors reoccupied the abandoned territories, but they were intolerable that the natives themselves invited the Arabs to liberate them from the Byzantine yoke. In response to their call, Muawiyah sent an army under the command of Okba Ibn Nafa who beat down all opposition and reduced the country to an Arab dependency. In 671, Okba built the famous military city of Kairawan, to the south of Tunis, to keep in check the fierce Berbers and to guard against the Roman ravages from the sea. In 676, Okba determined upon an advance into the West. The brilliant march of Okba and the crushing blows he inflicted on the Romans and Barbers made the country quiet for several years after which the Berbers surrounded Kairawan. Okba fought with a dauntless courage until he was killed. Kairawan fell into the hands of the Berbers and an Arab domination in Afrikia and the West seemed at an end. In 693, Abdel Malik Ibn Merwan sent an army for the reconquest of Afrikia under the command of Zuhair (a lieutenant of Okba). His operations were so eminently successful that he cleared the whole province of the enemy. But he was suddenly attacked by a large Roman army. The fight was desperate and the Arab general was killed and his soldiers cut into pieces. Afrikia again slipped out of the hands of the Muslims.
Intending to subjugate this land to Islam, Abdul Malik sent another army under Hassan Ibn Noman that for a time swept all opposition before it. Kairawan was recaptured and the city of Carthage was stormed. The Romans and the Berbers were defeated in open field. The remnant of the Roman army hastily abandoned the country and the Arabs were once more the masters of Barca to the shores of Atlantic. At that time, the Berbers acknowledged the authority of a woman called El Kahina (Divineress). For five years, El Kahina remained the Queen of Afrikia. The Arabs were overwhelmed, several detachments were cut to pieces, and the main army was once more forced back upon Barca. Abdul Malik sent another army under the command of Hassan. El Kahina was defeated and slain in a great battle at the foot of the Arabs. Being exhausted, the Berbers sued for peace which was granted to them. And now, Islam spread rapidly among the Berbers. In the reign of Walid Ibn Abdul Malik, Musa Ibn Nusair was made viceroy of Afrikia instead of Hassan. Hassan's withdrawal caused much disturbance, but Musa, by a series of daring operations pacified the whole country and conquered Morocco. Instructors were appointed to teach the people the principles of Islam. In a short time, all the Berbers were converted to the religion of Prophet Mohamed. Majorca, Minorca and Ivica were conquered and ceded to the Empire of Islam. These islands flourished under the Muslim rule.
Whilst Afrikia was enjoying toleration and justice under the Muslim rule, the neighboring peninsula groaned under the iron heels of the Goths. At the time when Musa ruled over Afrikia, the Iberian throne was occupied by Roderick who had deposed and murdered the former king, Witiza. Julian, the governor of Gueta, joined in the appeal of the Spanish refugees to Musa to liberate the country form the usurper's yoke. Musa, with the sanction of Walid, dispatched a young officer named Tarek Ibn Ziad, who landed with a small force of 7,000 picked men at a spot which now bears his name. In the meantime, his army had augmented to 12,000 men. Roderick was engaged in quelling a disturbance in the North, but the moment he heard of the invasion, he hurried to his capital. The number of the armies at his disposal reached 100,000, but the Gothic host was completely routed, and the king drowned in the waters of the Guadalete. The moral result of this magnificent victory was immense. It took the heart out of the Spaniards to meet the Arabs in the open. Malaga, Granada and Cordova fell one after the other without difficulty. After a short time, the whole peninsula was overrun by Musa and Tarek. Abdul Rahman el Ghfikki, once a viceroy of Spain, intended to conquer France; so he crossed the Pyranese and advanced in Southern France. But the Franks, under the command of Charles Martel, met the Arab host in the Battle of Toulouse in 732 in which Abdul Rahman was killed and a great number of the Arabs perished.
Downfall of the Ommeyades
The Ommeyades took great interest in politics and paid little heed to religion. Such a policy did not comprise the religious spirit of the Arabs. 2) Those of pure Arab origin were trusted by their lords and granted the high posts while the clients who were deprived of these privileges hated the dynasty, and never stopped plotting against the caliphs. 3) The Ommeyades were considered usurpers of the caliphate form Ali and his offspring. 4) The hatred of the Kharijis for the Ommeyades continued to raise disturbances all over the Empire. 5) Feud and disunion prevailed among the Ommeyade princes who rivaled one another. 6) The caliphs who succeeded Walid Ibn Abdul Malik were so powerless and weak that they could not overcome the factors of destruction all over the Empire. 7) Between the Himyarites and Modharites, there was a keen and constant antagonism verging on hatred. Although Muawiyah supported the Modharites, he was astute enough to hold the balance fairly and equally between them and the Himyarites that he did not allow the one to oppress the other. Under his successors, each party became preponderant and cruelly persecuted its rival.
You can get more information here.