From The Gospel of Matthew, by Curtis Mitch and Edward Sri, commenting on Matthew 2:1-12
The magi’s long journey reaches its climax as they enter the house and see the child with Mary his mother.
This reference to Mary and the child in a house in Bethlehem can stand in complete harmony with Luke’s account of the child being laid in a manger (Luke 2:7). Since first-century peasant homes in Palestine often had the lodging place for persons on one level and animals dwelling with a manger on a lower level, the house the magi visit in Matt 2 might be the same house where Jesus was born in Luke 2. Another possibility is that Jesus was born in a cave near Bethlehem (a tradition that goes back to second-century pilgrims traveling to Bethlehem) and that later the holy family moved to a more comfortable dwelling, a house, which is where the magi find them.
The magi do not simply kneel before Christ; they prostrated themselves on their faces and did him homage. Though prostration before kings was common in the ancient Near East, elsewhere in Matthew’s Gospel prostration and giving homage are associated with divine worship (4:9–10; 14:23; 15:25; 28:9, 17). The Gentile magi, therefore, offer Christ the worship that Herod, the chief priests, and scribes failed to offer.
The gifts of gold, frankincense (an expensive perfume used for incense in worship), and myrrh (an exotic spice) represent luxurious gifts fit for a king. They recall the Gentile queen of Sheba bringing spices and a large amount of gold for King Solomon (1 Kings 10:1–2). Jesus, the new son of David (1:1–17), is welcomed with similar gifts by these Gentile magi. The gifts also recall prophecies about the nations coming to pay homage to the king of Israel, falling down before him and offering gifts of gold and frankincense (Ps 72:10–11; Isa 60:1–6). As such, this scene underscores that Jesus is not just king of the Jews (2:2)—he is king of the whole world.