The first Roman attempt to conquer Parthia led by Crassus ended in disaster at the battle of Carrhae. His slow, heavy legions were surrounded and shot to pieces by fast, agile Parthian horse archers.
Centuries later the emperor Trajan invades Parthia and crushes the Parthian Empire, taking its capital, annexing most of the Middle East to the Persian Gulf, and appointing a client king subservient to Rome over what was left of the Parthian realm. For brief moment under Trajan it could be said that the limits Roman Empire (like that of Alexander) extended as far as the borders of India.
What troops, weapons, tactics did Trajan use that differed from those used by Crassus and why did they bring Trajan victory?
Crassus' defeat at Carrhae wasn't because Roman legions were somehow unable to fight Parthian armies. Crassus lost at Carrhae because he acted incompetently and marched into a desert--a fact that Plutarch has Cassius famously deliver a speech about. Crassus may not have been quite as incompetent at Carrhae as the orthodox view paints him, but the fact remains that he led an army deep into the desert improperly supplied, and then stood there and found himself unable to withdraw. About a decade later the Parthians were decisively and completely defeated by Publius Ventidius, who repulsed their invasion of Syria and Anatolia in a series of decisive battles. The army that the Parthians had invaded with even had a Roman commander, Cassius' buddy Quintus Labienus, and a sizable Roman force, the legions of Decidius Saxa, which defected to Labienus after Decidius was killed. Ventidius killed both Labienus and King Orodes' son Pacorus in battle and the Parthians fell apart. The Parthians were at peace with the Romans for most of the Principate, apart from some fighting over Armenia (in which the Parthians were soundly thrashed), and the history of warfare between the Romans and Parthians is one of the Parthians getting pretty decisively stomped every single time, with two exceptions. The one exception is Carrhae, and the other is Antony's disastrous invasion of Armenia, which failed not because of the Parthians (who basically didn't have an army anymore after Ventidius wiped them out) but because Antony decided to invade Armenia without proper supplies, and then retreated during the winter like a fool. The vast majority of his casualties were taken on the retreat, and not by enemy action. Plutarch reports that more than half of his losses were to disease, and Antony actually won every battle he fought with the Parthians during the retreat--Plutarch says specifically that the Parthians despaired that they couldn't break and scatter his army, and themselves were put to flight several times.
There was no difference in anything between Carrhae and the Armenian Expedition and the numerous and repeated defeats of the Parthians from Ventidius on except that the commanders were actually competent