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Also question is, did Rome ever defeat Parthia?
The wars between Rome and the Parthian Empire, which took place roughly from 53 BC to 217 AD, were a unique episode in classical history. Although Rome conquered nearly the entire civilized world around the Mediterranean, Rome could never conquer Parthia.
Furthermore, who defeated the Parthians?
In 53 BCE, the Roman general Crassus invaded Parthia. At Harran or Carrhae, however, he was defeated by a Parthian commander who is called Surena in the Greek and Latin sources, and must have been a member of the Sûrên clan. This was the beginning of a series of wars that were to last for almost three centuries.
Because it couldn't. The Parthian and Sassanian Persian Empires were too rich and too powerful, and too far away in real terms, to be destroyed by Rome; The Romans had a vast and sprawling dominion, that was vulnerable on a great many fronts, and was prone to internecine strife.