How do we know Christ is the fulfillment of Old Testament promises?

The scriptures reveal that Jesus is the fulfilment of many Old Testament promises and prophecies about the coming Messiah. In Luke 24:44, Jesus explains that everything written in the law, prophets, and Psalms must be fulfilled concerning Him. This theme runs from the first promise in Genesis 3:15, pointing to the seed of the woman who would crush the serpent, through to Isaiah's prophecies about a virgin bearing a son named Immanuel, who signifies God's presence among us. These prophetic declarations find their complete realization in the person and work of Jesus Christ.