Luk 2:1 In those days a decree went out from Caesar Augustus that all the world should be registered.
Luk 2:2 This was the first registration when Quirinius was governor of Syria.
Politically: Rome / Roman Empire
Religiously: The High Priest and His Party ( The Sadducees) and partially the Pharisees.
How was Istael controlled during jesus time:
Politically, the two Roman emperors during Jesus’ lifetime were Augustus Caesar, Tiberius Caesar and Herod the Jewish Kings of Palestine.
At the time of the birth of Jesus, the Romans had made Herod to be king over Israel. Herod was not a Jew. He was a foreigner. Although he was a Jew by religion, he did not obey the laws of the Jews, the Romans ruled Isreal through a line of proxy kings (the Herodians) and a regional governor (Pontius Pilate was one). Herod the “Great” wasn’t even truely Jewish in origin; his father was from Idumea. HG came to power through political intrigue, and by kissing up to the right people at the end of the Maccabbean revolt. Herod the Great ruled until shortly after Jesus’ birth. He rebuilt the Temple in Jerusalem, but was always fearful that he would be overthrown.
In the religious matters, the High Priest and his ‘party’ (the Sadducee) ruled the day at the Temple and in the Sanhedrin. They were kept in some sort of balance by the Pharisees, who sat on the same council.