The Census of Quirinius was a census of Judea taken by Publius Sulpicius Quirinius, Roman governor of Syria, upon the imposition of direct Roman rule in Judea in 6 CE. The Gospel of Luke uses the census to explain the birth of Jesus (Luke 2:1-5) in Bethlehem. However, the Gospel also places the birth of Jesus during the reign of Herod the Great, (Luke 1:5) who died nine years before the earliest possible date of the census. No plausible resolution of this contradiction seems possible, and most scholars think that the author of the Gospel made a mistake.
In 6 CE the Roman Empire deposed Herod Archelaus, who ruled the largest section of Judea as a Roman client king, and converted his territory into the Roman province of Judea. Publius Sulpicius Quirinius, the newly-appointed Imperial Legate (governor) of the province of Roman Syria, was assigned to carry out a tax census of the new province. According to Josephus, a Jewish historian writing in the late first century CE, Jews reacted negatively to this census. Most were convinced to comply with it by the high priest, but some joined a rebellion led by Judas of Galilee.
In those days a decree went out from Emperor Augustus that all the world should be registered. This was the first registration and was taken while Quirinius was governor of Syria. All went to their own towns to be registered. Joseph also went from the town of Nazareth in Galilee to Judea, to the city of David called Bethlehem, because he was descended from the house and family of David. He went to be registered with Mary, to whom he was engaged and who was expecting a child.-- (NRSV)
There are major difficulties in accepting Luke's account: the gospel links the birth of Jesus to the reign of Herod the Great, but the census took place in 6 CE, nine years after Herod's death in 4 BCE; there was no single census of the entire empire under Augustus; no Roman census required people to travel from their own homes to those of distant ancestors; and the census of Judea would not have affected Joseph and his family, living in Galilee. Some conservative scholars have argued that Quirinius may have had an earlier and historically unattested term as governor of Syria, or that he previously held other senior positions which may have led him to be involved in the affairs of Judea during Herod's reign, or that the passage should be interpreted in some other fashion. These arguments spring from the assumption that the Bible is inerrant and have generally been rejected on the grounds that there is no time in the known career of Quirinius when he could have served as governor of Syria before 6 CE, that the Romans did not directly tax client kingdoms, and that the hostile reaction of the Jews in 6 CE suggests direct taxation by Rome was new at the time. Most critical scholars have therefore concluded that Luke's account is erroneous.