Roman and Persian

While 

Roman Emperors like Trajan and Septimius Severuscaptured Persian capitals like Ctesiphon, a lasting conquest of the Persian Empire (Parthian then Sassanid) by Rome never occurred due to strong resistance, vast resources, and logistical challenges, with victories often short-lived; the long conflict ended with both empires falling to Arab conquest, though Rome (Byzantines) ultimately had more success in the final wars. 

Key Figures & Events:

• Emperor Trajan (Roman): Overran the Parthian capital Ctesiphon around 116 AD, installing a client king, but rebellions forced a Roman withdrawal.
• Emperor Septimius Severus (Roman): Sacked Ctesiphon in 198 AD but couldn't take Hatra, and the territory wasn't permanently held.
• Emperor Shapur I (Persian): Inflicted a massive defeat on Emperor Valerian at Edessa in 260 AD, capturing the Roman Emperor – a shocking event.
• Emperor Galerius (Roman): Defeated Persians, captured Ctesiphon, and secured significant Mesopotamian territory for Rome in 298 AD.
• Emperor Julian (Roman): Died leading a major expedition against the Sassanids in 363 AD, resulting in territorial losses for Rome after a treaty. 

Why No Roman Conquest?

• Military Parity: Parthian and Sassanid Persia were formidable military powers, often matching Rome's strength.
• Logistics: Campaigns deep into Persia were difficult and risky.
• Lack of Incentive: Neither side fully sought to annex the other's vast empire, focusing more on border control and buffer states. 

Outcome:

The prolonged Roman-Persian Wars (or Roman-Iranian Wars) ended with neither side conquering the other permanently, with both eventually succumbing to the rising Islamic caliphates in the 7th century.