The demise of the Hasmoneans and the rise of the Herodians in the first century BC happened by virtue of the expansion of Roman imperial power in the east. When the Seleucid Empire disintegrated, the Romans moved in, and Syria became the center of Roman power in the east. As a result, Syro-Phoenicia, Galilee, Iturea, Perea, and Judea, constituted the southern land bridge linking Syria and Egypt, which gave it strategic importance. The Romans also had influence over Armenia, nominal control over several cities in the Trans-Jordan and along the Euphrates, and over client kingdoms such as Nabataea.
As the Romans took control of the Levant (i.e the eastern Mediterranean coastal region), Roman power interposed itself in Judea in 63 BC when Pompey intervened in a civil war between the Hasmonean princes Hyrcanus II and Aristobulus II. Pompey captured Jerusalem, made Judea a client kingdom under Hyrcanus II, and incorporated it into the Roman province of Syria. While Judea maintained limited autonomy under its priest-king rulers, it was now effectively under Roman hegemony.
Then, in 40 BC, the Parthian Empire made a surprise incursion into Syria and Judea, temporarily seizing Antioch and Jerusalem. In Judea, the Parthians installed Antigonus, the last Hasmonean ruler, as king. The Romans responded by appointing Herod as King of Judea (though the extent of his kingdom was not known at that point). Herod, with Roman military support, re-captured Jerusalem in 37 BC, married a Hasmonean princess, wiped out the rest of the Hasmonean line, and established his reign under the aegis of Roman rule.
After Herod's death in 4 BC, his kingdom was divided among his surviving sons (Herod had killed most of his other sons): Archelaus received Judea and Samaria, Herod Antipas got Galilee and Perea, and Philip received territories east of the Jordan. However, Archelaus proved to be an ineffective ruler, and in 6 AD, Augustus removed him and converted Judea into a Roman province under direct imperial control, administered by prefects (later procurators).
Thereafter, it gets a bit complex with Herod Antipas losing his territories, brief periods of direct Roman rule through prefects, and Herod Agrippa I and Herod Agrippa II both having periods of ruling over various parts of Judea, Galilee, and nearby territories.
Remember, the Romans did not occupy Judea the same way that America occupied Afghanistan. The main military force was in Syria with the Legate, the Roman prefect of Judea had a small force at Caesarea-Maritima, Antipas and Agrippa I & II had their own mercenaries and private guard, while the High Priests in Jerusalem had their temple guards or thug-squad.
A rebellion eventually began against Roman rule in 66 AD. But why?
Several theories exist as to why the Jews chose to rebel in AD 70.