How does Old Testament prophecy point forwards to Jesus Christ?
As the nation of Israel went into its long period of division, decline and decay following the rules of David and Solomon, God sent a series of messengers calling his people to turn back to him.
These messengers, the prophets, warned the people of Israel and Judah of judgment to come if they continued to turn away from God into false religion and idol worship. But they also looked beyond the coming judgment, to a future restoration in which God would send a promised deliverer, the Messiah. Although their main ministry was to call people to turn back to God, a large part of what they said described what would happen in the future.
The first of the prophets was Elijah. He began a new stage in the development of God's revelation in the Bible. He was followed by Elisha. Neither of these prophets left a written record of their messages, but the later prophets are called 'writing prophets' because they have left a written record in Old Testament books such as Isaiah, Jeremiah, Ezekiel and Daniel, and the 'minor prophets' (so called only because their books are shorter) - Hosea, Joel, Amos, Obadiah, Jonah, Micah, Nahum, Habakkuk, Zephaniah, Haggai, Zechariah and Malachi.
The important thing about the prophets is that they were not just giving their own opinions about what would happen - they had a message from God. So the key phrase in their writings is 'This is what God says..' or 'This is the word of the Lord.'
After the Jews had been in captivity in Babylon for about seventy years, they were allowed to go home by the Persian emperor Cyrus. Back in their own land, they rebuilt the walls of Jerusalem and the temple, and re-established the sacrificial system. These events are recorded in the Old Testament books of Ezra and Nehemiah. However, what happened was only ever a very partial fulfillment of the prophecies of restoration, and the people continued to look forward to the future coming of the Messiah.
There are many specific prophecies about the Messiah in the Old Testament that were fulfilled in detail by Jesus Christ. For the past two thousand years, followers of Christ have seen these as an important part of the overall evidence for the truth of the Bible's message.
In some cases, it is clear that Jesus deliberately set out to fulfill an Old Testament prophecy. This may make its fulfillment less convincing to someone who does not believe (although it still provides important evidence about how Jesus himself understood his relationship to the Old Testament). But there are other prophecies that he could not have deliberately fulfilled, for example that the Messiah would be born in Bethlehem (Compare Matthew's Gospel chapter 2 verses 1-6 with Micah chapter 5 verse 2).
Mostly the Israelites expected the Messiah to be a ruler and a military leader who would deliver them from oppressive foreign powers. But there was another key strand in Old Testament prophecy that foresaw the Messiah as a 'suffering servant' who would deliver his people through his own pain and sacrifice. The clearest expression of this is found in the 'Servant Songs' of Isaiah chapter 42 verses 1-4; chapter 49 verses 1-6, chapter 50 verses 4-9 and chapter 52:13-53:12:
Psalm 22 contains a remarkably accurate description of Jesus's crucifixion Yet these words were written hundreds of years before Jesus was put to death, and crucifixion was a Roman way of execution, not Jewish, unknown in Israel at the time this Psalm was written. Jesus took up the opening words of the Psalm in his cry from the cross, 'My God, my God, why have you forsaken me?'
These are just a couple of examples. There are many others. The 'New Evidence that demands a Verdict' by Josh McDowell has a long section (pages 164 to 202) setting out Old Testament Prophecies that were fulfilled in Jesus Christ.
Problems with predictive prophecy
Many of the things that the Old Testament prophets foretold were fulfilled in remarkably accurate detail. Because of this, scholars who do not allow for the possibility that God really spoke supernaturally about future events have sometimes insisted that the books in question must have been written later, after the events they foretold.
There is no reason for this late dating, other than the prior assumption that the prophets could not possibly have foretold the future accurately. In some cases, more recent scholarship has shown that a later dating for the book in question is impossible, or extremely unlikely, for example on linguistic grounds. Not only that, but Old Testament prophecies that were fulfilled by Jesus Christ could not have been written after the event - the Old Testament was finished several hundred years before Christ was born, and was already widely circulated in his time. Next.
For more about how the whole Bible points to Jesus - Old Testament as well as New Testament - read Vaughan Roberts' excellent book 'God's Big Picture: tracing the story-line of the Bible', or Graeme Goldsworthy's 'According to Plan: the unfolding revelation of God in the Bible', or Alec Motyer's 'Look to the Rock: An Old Testament Background to our understanding of Christ.'