Isaiah has at least eighteen direct messianic references. And by some counts, Isaiah’s prophecy is referred to over four hundred times in the New Testament. J. Alec Motyer says, “The Isaianic literature is built around three messianic portraits: the King (chapters 1-37), the Servant (chapters 38-55) and the Anointed Conqueror (chapters 56-66).”
One example from Isaiah’s portrait of Messiah as king is found in Isaiah 11:1-10.
There shall come forth a shoot from the stump of Jesse,
and a branch from his roots shall bear fruit.
Notice this figure is a king who judges with equity (vv. 3-4), destroys the wicked who oppose him (vv. 4-5), and will bring knowledge of Yhwh (v. 9). Then in verse 10, the idea of a shoot from the stump is repeated:
In that day the root of Jesse, who shall stand as a signal for the peoples—of him shall the nations inquire, and his resting place shall be glorious.
So Isaiah sees this messianic world-savior king as a root of Jesse; Jesse’s true offspring, the greater David. The tree of Israel has been chopped off in judgment so that only a stump remains. But from that stump a tender shoot comes forth. And what was Israel’s hope? “There shall come…”
“There sounds out from the oldest to the latest sources…the mighty ‘he comes’ (cf. Gen 49:10), ‘he appears’ (Num 24:17), ‘he cometh’ (Zech 9:9), ‘he is born’ (Is 7:14; 9:4), ‘he comes forth (11:1), ‘he comes forth (Mic 5:1), ‘he is raised up’ (Jer 23:5), ‘until he comes’ (Ez 21:32), ‘I will raise up’ (34:23), ‘I bring’ (Zech. 12:8), ‘I saw, there come’ (Dan. 7:13).” This continually recurring assurance that the Paradise-prince will come to destroy all enemies and judge even to the ends of the earth, forms the deepest core of the mystery—it is expressed by a single word in Hebrew, in English, “He comes.” It stamps the religion of the Old Testament as specifically a religion of hope.
The ultimate answer to Isaiah 11 comes in Revelation 22:7, “Behold I am coming soon.” And 22:12, “Behold I am coming soon.” And again 22:20, “Surely I am coming soon.” And who is it that is coming? He identifies himself in 22:16,
“I, Jesus, have sent my angel to testify to you about these things for the churches. I am the root and the descendant of David, the bright and morning star.”
Christian have a messianic hope still today. Certainly we have an advantage in the fullness of Scripture. We have not only Isaiah but also Revelation. But we can certainly understand the psychology of hope/anticipation that existed in Israel. Our worldview is not so very different from theirs.
We are still looking forward to a future world in which a world-saving king will reign, and will right all the wrongs, and will reverse entropy, and will establish harmony. All the things Isaiah wanted as Israel was on the verge of exile are the same things that we want and foresee as we are in the midst of exile.
And so the Christian ends where Isaiah points and Revelation ends, “Even so, come Lord Jesus!” (Rev. 22:20)
 Walter C. Kaiser, The Messiah in the Old Testament, 155-156.
 J. Alec Motyer, Isaiah: Introduction and Commentary, 13.
 B. B. Warfield, “The Divine Messiah in the Old Testament,” here he is both quoting and distilling Ernst Sellin.