Persian Empire refers to any of a series of imperial dynasties centered in Persia (modern–day Iran). The first of these was established by Cyrus the Great in 550 BC with the conquest of Media, Lydia and Babnia. It covered much of the Ancient world when it was conquered by Alexander the Great, after his death divided in diadoch realms. Several later dynasties "claimed to be heirs of the Achaemenids". Persia A.K.A. Iran was then ruled by the Parthians whom drove out their Greek invaders, and then by the Sassanians whom ruled up until mid 7th century anno domini.
Persian dynastic history was interrupted by the Arab Muslim conquest of Persia in 651 AD, establishing the even larger Islamic Caliphate, and later by the Mongol conquest of Khwarezmia.
The main religion of ancient Persia was the native Zoroastrianism, but after the seventh century, it was replaced by Islam.
In the modern era, a series of Islamic -notably Shiite- dynasties ruled Persia independently of the Arab/Turkic Sunni caliphates, who became Persia's classical rival, like the pagan Romans and Christian Byzantines had been before.
Since 1979 and the downfall of the Pahlavi dynasty, Iran A.K.A. Persia has a Shiah theocratic Islamic dictatorship.
Muslim conquest of Persia (633–654) - part of the Arab first caliphate
Mongol conquest of Khwarezmia (1218–1221) - pagan