The Umayyad Caliphate saw a period not only of expansion, but also of unification and reform. One example was when an earlier policy of paying stipends to retired military and their descendants was deemed an untenable drain on financial resources and was eliminated in favor of only paying active military.
The Byzantine gold solidus—a standard in the eastern Mediterranean and beyond—was replaced in 693 by the dinar (see an example here). The dinar originally had the head of the caliph on it, but this use of images lasted only a few years before religious objections replaced it with quotations from the Koran. Other coinage used in Muslim-ruled lands also had imagery replaced in the next few years.
Arabic became the official language of all territories of the caliphate, and government officials who spoke Persian and Greek needed to learn Arabic to keep their posts.
The Dome of the Rock was completed in Jerusalem in 691/692. Although Mecca retained importance for Muslims, it is thought that the Umayyad creation of the Dome of the Rock was intended to take some of the importance away from Mecca, since the Umayyads were originally condemned in Mecca by those faithful to the previous Rashidun Caliphate.
The Umayyad expansion consolidated all of Northern Africa and moved into the Iberian Peninsula. It is their presence in Spain that led to the first big clash with Western Europe, when in 721 Odo the Great fought them at the Battle of Toulouse. I'll tell you about Toulouse tomorrow.