The second thing that only Matthew, (and no one else) records is:  (I hope you will get your Bible and read these accounts for yourself.) 
Number 2 :  The visit of the Wise Men.  Matthew 2:1-12 "...there came wise men from the east to Jerusalem saying, Where is he that is born King of the Jews? For we have seen his star in the east and are come to worship him."  Herod, the king, drew all the priests and scribes into his chamber to hear what the wise men said, and asked where this Messiah would be born.  They told him:  Bethlehem.

They quoted what Micah, the prophet had foretold.  Micah 5:2 "But you, Bethlehem, you are little among the thousands of Judah.  But out of you shall he come that shall be the ruler in Israel; whose goings forth have been from of old, from everlasting."  So Herod sent the wise men on their way to Bethlehem to find the child and bring back word so that he could go there and worship him, too.  (But his plan was to kill him--he didn't need a rival ruler.)

A decree from Caesar had forced everyone to go the city of their lineage to pay taxes.  Joseph was a descendant of King David, so he and Mary went to Bethlehem.  Eight and a half months pregnant, riding on a donkey.  Mercy.  Our King was born in a barn.  Talk about humble. 

So the wise men followed the star going before them which came and stood over where the young child was. They fell to their knees and worshiped him, and gave him gold, frankincense, and myrrh.  A regular church service.  The first Christmas gifts. They (the Wise men) then had a dream warning them about Herod's intentions.  So they left and went back to their own country by a different route.

Matthew gave us a wonderful story that we wouldn't know about if he hadn't written it down.
Thank you Matthew.  

Sometimes you just need to follow your star.  Who knows what you'll find.