The Achaemenid Persian empire, centred on Persia, was destroyed by Alexander the Great. After his death, the eastern parts were inherited by one of his generals, Seleucus, who established a dynasty running down from ca. 300 BC to Pompey's campaign in 68 BC. But their history is one of loss of territory. The eastern satrapies fell to a group of horse-nomads, akin to the scythians and huns, who were known as the Parthians, mainly because of Seleucid weakness. By the end of the Seleucid period they controlled from Mesopotamia to Bactria, including old Persia. They remained the main eastern foe of the Romans, although they were not aggressive and contented themselves mainly with destroying Roman invasions. Their capital was at Ctesiphon. Their kings belonged to the Arsacid dynasty, descended from Arsaces.
But the Persians had not gone away, and a Persian client kingdom continued to exist. Ammianus Marcellinus records the fall of the Parthian rule in the third century, after the Parthian king Artabanes was humiliated by Caracalla (it's online). The Persians organised an insurrection and overthrew the Parthians, creating the Sassanid dynasty. This was a much more aggressive, much more tightly knit state, and its first action was to lay claim to the entire Achaemenid domains, including all of Asia Minor, and to attack the Romans.
The Arsacids remained in control in Armenia. But the Sassanids were a constant foe draining Roman power for centuries. They were eventually completely defeated by the emperor Heraclius by 630 AD after a ruinous war that left both sides exhausted. Unfortunately in the next few years the Arabs poured out of the desert, and neither the Romans nor Sassanids could resist. The Sassanids were swept away and their empire became part of the Ummayad caliphate.
But this wasn't the end of the story. Persia still existed, and there was a strong feeling among Persians that they had been caught from behind, and a desire for a rematch. This came to a head after a century or so, when there was a general rising against the last Ummayad caliph, Marwan II, led by men from Khorassan. A very vivid eye-witness account of Marwan's desperate attempts to raise money and supplies in Egypt as the Persians hunted him down can be found in the
History of the Patriarchs of the Coptic Church of Alexandria (online at my site).
The Ummayads were overthrown, and a new dynasty of Abbasid caliphs took their place. These were Persian, and arrogant with it apparently, and they moved the capital from Damascus to Baghdad. The Abbasid caliphate is the East of the
Thousand and One Nights, of Haroun Al'Raschid, etc.
I hope these hasty notes help you.
All the best,
Roger Pearse