It is not a secret that we know less about the Magi mentioned in the Gospel of Matthew than is popularly portrayed.
- The number of them is not mentioned in the Gospels, just the number of gifts.
- They were not kings.
The one fact that I though that we did know was that likely they were from Persia because of the use of the term Magi.
Fr. Dwight Longenecker in his new book Mystery of the Magi: The Quest to Identify the Three Wise Men takes a dive into the history concerning this and comes up with some interesting answers. I found it a very worthwhile read. I enjoyed how he pieces together the clues and sets up the possible solution. He challenges both the scholars who think the visit of the Magi were not historical and those who thought the case they were from Persia was strong. He does it in such a way as to not saying his theory is the definitive answer, but to advance scholarship on this.
There was also some coverage regarding various theories regarding the Star of Bethlehem and it does a good job of covering in summary form some of these theories. The only weakness I found in this was a dependence of Herod the Great dying in 4 B.C., which has been commonly held. This dating is important in regards to various theories based on astronomy. Jimmy Akin has a good article regarding this dating which puts Herod’s death a couple years later Jesus’ birth and when Herod the Great really died.
Here is a recent article he wrote regarding his book.
Here is a review by Thomas L. McDonald in the National Catholic Register.