The Sasanian Persian Kingdom
Seleukos I Nikator emerged as ruler of Alexander's Eastern conquests, an area (including most of the former Persian Empire) that Alexander himself would have been very hard pressed to defend. This realm proved to be far beyond the capability of Seleukos' heirs to control.
The first evidence of this was the defection of Diodotus, satrap of Bactria and its surrounding provinces, whose secession founded the Greco-Bactrian Kingdom around 250 b.c. The next was the defection of Andragoras satrap of Partahia, who briefly ruled until the Skythian Parni tribe led by its chieftan Arshak founded the Parthian Kingdom in 238 b.c.
The Parthian Kingdom, which endured for more than four centuries, ultimately could not cope with repeated Roman invasions. It was cordially hated by Persian nobility who regarded Parthians as barbarians. After a very destructive invasion Ardashir I, king of Persis, rebelled and defeated Artabanos V in 224, establishing the Sasanid Kingdom which ruled until the seventh century.
This became the most powerful Persian state since the Achaemenid Empire, confronting the Roman Empire in a manner far more menacing than the Parthians ever did. Adding a disciplined infantry corps, siege train and armored lancers to nomadic horse archers resulted in a versatile and effective Persian army, whose capabilities approached those of the Roman military.
The triumph of Shapur I (241-272):
This most famous of Sasanid rock reliefs depicts Shapur's victory over three Roman emperors, Gordian III, Valerian and Philip the Arab. A more elaborate version is at Bishapur. Shapur I very nearly destroyed the Roman Empire when he captured Valerian and the Roman field army in 260 at the Battle of Edessa, and may be considered as being the greatest pre-Islamic Persian king. A powerful and characteristic portrait of Shapur I may be viewed (and acquired) here: