At around 250 BCE, a nomad warchief, Arsaces, lead the (probably) iranian Parni tribe from their homeland between the Caspian and Aral seas into the Seleukid satrapy of Parthia, whose governor, Andragoras had recently rebelled against the king (its not clear whether it was Antiochos II or Seleukos II, since the succession took place in 246 and the precise date of the rebellion is unknown). Few years come and Arsaces has managed to defeat and kill Andragoras and establish himself as a local power.

Seleukos II would, later, march against Arsaces to try and regain his control over the area, having mixed results, though it seems like the Parni managed to reassert their autonomy. This would come to an end in 209, when Antiochus III defeated Arsaces II, forcing him into a vassal status.

This condition, however, was not to last long, especially after Antiochos' defeat against Rome and the progressive weakening of the Seleukids. The following Seleukid monarchs led campaigns to the East, but were met with the strong leadership of king Mithradates I, who defeated Demetrios II and Antiochos VII. By the end of his reign, in 138, the Parthians had kicked the Seleukids out of Iran and conquered most of Mesopotamia, and during the following decades and prior to the start of Roman presence in Syria, they would consolidate their dominion and also expand eastwards, becoming the major power of the Middle East and, since Crassus' failed campaign in Carrhae, Rome's main enemy.

What happened between Crassus and the deposition of the last King of Kings of the Arsacid dynasty, Artabanos IV, was a series of confrontations against the Romans, first against the Republic, then, against the Principate. One of the main problems behind these wars was the control of the Caucasus, this is, the kingdom of Armenia, which ended up being ruled by relatives of the King of Kings, but under Roman approval.

Despite this, peace was never really the norm, since no power could ever assert their full dominance over the other: the most successful offensive Parthian campaign barely managed to briefly control Syria and Palestine for some years during the times of the Second Triumvirate (and only because they had local help), and while various Roman emperors managed to sack Ctesiphon, the Arsacid royal city, and Trajan even conquered the whole of Mesopotamia, roman advances into the East were never completely successful due to various reasons and the frontiers kept a more or less stable line for more than three hundred years (though they suffered more changes in Armenia and northern Mesopotamia, where a number of small buffer principalities, such as Adiabene or Oshroene, existed for a long time).

Eventually, the Arsacids were deposed and the Sassanian dynasty inaugurated a much more agressive policy against Rome, of which Shapur I and II and the later Khosrow I and II are splendid examples.

As for sources, and while not a lot has been written on the Arsacids, you have Cam Rea's "The Rise of Parthia in the East" and Overtoom's "Reign of Arrows", focusing on the first two centuries of existence of the empire, Rawlison's "History of the Parthian Empire" for a more in depth view of the empire, and also Ellerbrock's "The Parthians: The Forgotten Empire". Lastly, you may find interesting Cam Rea's "Leviathan vs Behemoth", which focuses on the wars between the Arsakids and Rome. These are all relatevely easy to find in online stores, and from them you should be able to dive down into more sources and bibliography.