Jesus’ birth and infancy are described in the Gospels of Matthew and Luke, but are not even mentioned in Mark and John.
Moreover, the infancy narratives in Matthew and Luke are seemingly quite different from one another. Luke mentions the census of Quirinius which requires Joseph to go to Bethlehem where Jesus is born in a manger because there is no room at the inn. Matthew, however, gives no details of how Joseph and Mary came to be in Bethlehem; nor are there any details of Jesus’ birth.
In Luke, shepherds guided by an angel find Jesus in the manger; they praise God for what they have seen but do not bring the child gifts. In Matthew, wise men from the East, guided by a star, come not to Bethlehem but to Jerusalem to worship the Infant. Herod hears of the wise men from the East and sends them to Bethlehem to learn and report to him about the Infant. The wise men unlike the shepherds in Luke bring the Infant gifts of gold, frankincense and myrrh, but, warned by an angel, return to their own country instead of reporting to Herod. Warned by an angel that Herod intends to kill the child, Joseph flees with his wife and child to Egypt where they live until Herod’s death; then they return to Nazareth instead of Bethlehem.