The Census of Quirinius was a census of Judaea taken by Publius Sulpicius Quirinius, Roman governor of Syria, upon the imposition of direct Roman rule in 6 CE. The Jewish historian Josephus portrays the annexation and census as the cause of an uprising which later became identified with the Zealot movement. The author of the Gospel of Luke uses it as the narrative means by which Jesus was born in Bethlehem (Luke 2:1-5), and places the census within the reign of Herod the Great, who actually died 10 years earlier in 4 BCE. No satisfactory explanation has been put forward so far to resolve the contradiction, and most scholars think that the author of the gospel made a mistake.
In 6 CE Publius Sulpicius Quirinius (51 BCE-21 CE), a distinguished soldier and former Consul, was appointed Imperial Legate (governor) of the province of Roman Syria. In the same year Judea was declared a Roman province, and Quirinius was tasked to carry out a census of the new territory for tax purposes. The new territory was one of the three portions into which the kingdom of Herod the Great had been divided on his death in 4 BCE; his son Herod Archelaus was given Judea but complaints of misrule prompted his removal and Judea and Samaria were placed under direct Roman rule, although Galilee and other areas remained autonomous.
The Gospel of Luke places the birth of Jesus under the reign of Herod (37 BCE - 4 BCE) - "In the days of King Herod of Judea..." (Luke 1:5) and links it to the census of Quirinius: