One of the most important things anyone has ever said about Scripture is:
Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them.
–Jesus in Matthew 5:17
The careful reader of Matthew will hear “fulfill” in 5:17 and recall at least some of its previous uses already in the book.
Fulfillment is one of Matthew’s major themes. Calling the other uses of “fulfill” to mind gives Jesus’ claim even more impact.
Having established that Jesus’ birth was “to fulfill what was written…,” Matthew shows John baptizing an adult Jesus “to fulfill all righteousness.” Early in Jesus’ ministry, Matthew shows Jesus as the fulfilling light that the people walking in darkness have been waiting for.
Here is a one-page pdf listing the instances of fulfillment in the birth and early ministry of Jesus in Matthew 1-4.
With so much of his life a fulfillment of the Scriptures already, Matthew’s reader is now prepared to see how Jesus fulfills all of Scripture–down to the last letter–through his read and interpretation of it. In the rest of Matthew 5, Jesus will unpack just what he means by “fulfill [the Scriptures],” using six specific biblical examples, culminating at last in a call to the disciples to “be perfect.”
Words on the Word 
You might be interested in the article “‘The Virgin Will Conceive’: Typological Fulfillment in Matthew 1:18-23” found in the book “Built Upon Rock: Studies in the Gospel of Matthew” edited by Gurtner and Nolland. It is an interesting study of the meaning of “fulfill” for Matthew.
Thanks for the recommendation! I’ll check it out.