Arabic/Islamic civilization is one of three cultures that succeeded the classical period of Greece and Rome. However, this civilization, unlike the Byzantine Greek and the Latin West, did not just inherit from the classical civilizations of Greece and Rome; it also inherited a great deal from the empire that it had completely conquered, the Sassanian Persian.
The last and largest of the great middle eastern empires before Alexander the Great was the Persian Empire, often referred to as the Achaemenid Empire (after a Greek form of the name of the dynasty that ruled it). Alexander the Great conquered it in 331 B.C.E. and the area was subsequently ruled for a time by his general Seleukos and his descendants, what is known as the Seleucid Empire. However, another Iranian people, the Parthians, founded a new state in what had been eastern Persia. Its founder was one Arsaces I who established the new Parthian state in 248-247 B.C.E. As time passed, the Parthian Empire gradually conquered all of the Seleucid Empire except the regions along the Mediterranean coast which were conquered in turn by the Romans.
Iran, Ancient Persia, stands as a bridge between East and West, a fact which has not only influenced her religion, but has also made Iran a watershed of history. Western Iran was influenced by Mesopotamia, Greece and Rome, and Eastern Iran was influenced by India and even China since the ancient trade routes cross-pollinated those cultures. As an interesting fact of history, we could have had a vastly changed religious prospect for the Western world, had it not been for the defeat of the Persian King Xerxes in the Battles of Marathon and Salamis.