I am a student of ancient history as it pertains to the Bible, and while that may seem pointless to some, it fascinates me for some reason. Call me crazy, but I like reading the Works of Josephus and various other historical narratives from our past. I actually have Antiquities of the Jews open in front of me as I write this. Notably, I'm looking at Book 17, chapter 2, verse 42--"Accordingly, when all the people of the Jews gave assurance of their good will to Caesar, and to the king's government, these very men did not swear, being above six thousand..." Josephus is writing about the Pharisees who refused to swear allegiance to Augustus Caesar, and so Herod (you may know him as the baby killer) imposed a fine on them.
Some scholars agree (and I agree with them) that this is a reference in passing to the "census" mentioned in Luke 2:1-2:
"And it came to pass in those days, that there went out a decree from Caesar Augustus, that all the world should be taxed. ([And] this taxing was first made when Cyrenius was governor of Syria.)" (KJV)
What has puzzled scholars for years is the fact that our English versions tend to place the census during the governorship of Quirinius, but Quirinius did not come to Syria as governor until after Herod was dead and Archelaus, Herod's son, needed to be dealt with. By that time, Jesus would have been in elementary school in Nazareth, and so there seemed to be a major historical discrepancy here. Some reasoned that Quirinius had a "first" governorship that archaeologists have not yet discovered. But there is a much simpler explanation.
Yes, there was a census under Quirinius after Judaea became a part of the province of Syria, and this is from what Luke is trying to make distinction. The Greek word protos, which is usually translated as "first" can also indicate "before" in matters of time. For example, the Pharisees knew "Elijah" would come first and then the Messiah would come (Matthew 17:10, cf. Malachi 4:5). In other words, "Elijah" would come before the Messiah.
The way I understand Luke 2:2, Luke is telling us of a census or taxing that happened before Quirinius was governor of Syria so that his original reader, Theophilus, would not be confused with the census that happened after Archelaus was deposed much later after Herod had already passed away.
Augustus himself notes that in his 13th consulate (2 B.C.), the Senate and all the people called him "father of the country". This was great cause for a census/registration and what Josephus notes (what I referenced above). This was certainly what would have brought both Joseph and Mary to Jerusalem and to Bethlehem as they were both descendants of David.
This is how I would translate Luke 2:1-2:
"Now it happened in those days that Caesar Augustus issued a decree that the whole of the inhabited earth should be registered (this registration happened before Quirinius was governor of Syria)..."
