Quirinius

Roman "governor" of Syria whose census just before the death of Herod the Great was the occasion for Joseph and Mary to return to Bethlehem where Jesus was born (Lk 2:2).

Luke has, according to his own testimony, "carefully" researched his sources in composing his gospel, and he uses several historical persons, including Quirinius, to pinpoint the exact moment of some of the events he has reported. Things seem pretty straightforward as it is, except that the Jewish historian, Josephus, also reported about Quirinius' census, but, by his reckoning, the census took place long after the death of Herod. This has puzzled historians and issued in an enduring debate. It is the general consensus among historians that Luke is out of kilter; Daniel Schwartz, of the Hebrew University, Jerusalem, e.g., declares that it "seems fair to say that the scholarly consensus today, shared even by many conservative Christian scholars, is that Luke is wrong." That conclusion may not be the end of the story, however. First, Josephus is not an altogether reliable historian, and is known to repeat the same incident in different sources as two separate events. Additionally, Tertullian spoke of the census being carried out by Saturninus, governor of Syria 9-6 BC. Archaeology, also, has often turned out to favour the biblical assertions when scholars have long thought it wrong. The debate is too complex for a meaningful summary; below are some resources if you are interested in the debate.

Quirinius whose full name was Publius Silpicius Quirinus was also known as Cyrenius. He died in 21 AD and was buried with full honours on the request of Emperor Tiberius, of whom he was a favourite.

Resources:

Wayne Brindle, "The Census and Quirinius: Luke 2:2," Journal of the Evangelical Theological Society 27/1 (Mar 1984): 43-52.
Pdf N 6 (Open on Phone)

Jared M. Compton, "Once More: Quirinius’s Census," Detroit Baptist Seminary Journal 14 (Fall 2009): 45-54. Pdf N 5-6 (Open on Phone)

John Rhoads, "Josephus Misdated the Census of Quirinius," Journal of the Evangelical Theological Society 54.1 (Mar 2011): 65-87.
Pdf N 6-7 (Open on Phone)

David Wenham, Luke Acts: The Quirinius Issue Youtube
(Open on Phone)