Growing up in the Armstrongite tradition, I heard about Nebuchadnezzar's dream of the image in Daniel 2 over and over again. It was also emphasized in an independent Seventh-Day church that I attended. I continually learned and relearned that the head of gold was Babylon, the chest and arms of silver represented the Medo-Persian empire, the belly and thighs of bronze were the Greek empire, and the legs of iron and feet of iron and clay were the Roman empire. In Daniel 2, a stone from heaven lands on the feet of the statue, thereby shattering the entire image and making it like chaff. My Armstrongite heritage maintained that this means that Christ would return when the revived Roman empire----a United States of Europe----was holding sway, for (according to Armstrongites and others) the Roman empire is destroyed in Daniel 2, and that must indicate that there will be a Roman empire when Christ comes back.
As I look at wikipedia's article (see here----and I will not publish comments giving me flack over using wikipedia), I see that some groups differentiate between the legs of iron and the feet of iron mixed with clay. Jehovah's Witnesses, for example, suggest that the legs of iron are Rome, whereas the feet are the Anglo-American World Power. Seventh-Day Adventists maintain that the legs are Rome, and that the feet are a global religio-political government.
What I got from my reading of historical-critics of the Bible was different: the head was taken to be Babylon, the chest and arms to be the Medes, the belly and thighs to be the Persians, and the feet of iron and clay to be the Greeks and empires descended from them. The idea was that Daniel 2 reflects the hope that God would overthrow the Seleucid (Syro-Greek) tyrant, Antiochus Epiphanes, thereby vindicating Israel and ending Gentile domination over her.
Something that my Dad brought to my attention years ago was that the rock from heaven does not just shatter the fourth (or fifth) kingdom; rather, it destroys the entire image. This reminds me of Revelation 13, where the Beast is presented as a combination of the animals of Daniel 7, who represent world empires that had dominion over Israel. What is the significance of the entire image being reduced to dust? I can think of various answers. The entire image represents Gentile dominion over Israel, and that collapses when God sets up his kingdom. The entire image symbolizes the evil world system, which has existed for centuries and which God will bring to an end. The Beast will resemble (and embody) and yet surpass in viciousness his predecessors. And the list can go on.
It was interesting to see an attempt to wrestle with the issue of the entire image collapsing in The Cambridge History of Judaism, Volume Two: The Hellenistic Age. H.L. Ginsberg (a legend who taught at one of my alma maters, Jewish Theological Seminary) addresses this topic in his article on Daniel. On page 511, Ginsberg argues that Daniel 2 had to have been written when the four kingdoms were still standing, in some form-----when there were at least remnants or petty kingdoms of Babylon, the Medes, the Persians, and the Greeks. After all, does not v 44 say that God will set up his kingdom in the days of those kings? Consequently, Ginsberg looks for a time that fits this bill. In 310-circa 301 B.C.E., the territory of Seleucus I centered on Babylon and technically was not a part of the Greek kingdom, which was "a bone of contention among Ptolemy, (Demetrius son of) Antigonus, Cassander, and Lysimachus" (page 512). That, for Ginsberg, was when much of Daniel 2 was written. The four kingdoms (Babylon included) were standing on some level, and there was an expectation that God would overthrow all of them.
But Ginsberg believes that an interpolation, vv 42-43, disrupts this picture. These verses say (in the King James Version): "And as the toes of the feet were part of iron, and part of clay, so the kingdom shall be partly strong, and partly broken. And whereas thou sawest iron mixed with miry clay, they shall mingle themselves with the seed of men: but they shall not cleave one to another, even as iron is not mixed with clay." Ginsberg interprets these verses in light of the events of 252-246 B.C.E., when there was an unsuccessful attempt to fuse the Seleucids and the Ptolemies through marriage. In this interpretation, vv 42-43 present the Seleucids as "a part of the divided Greek kingdom", which extend from the legs of iron, whereas vv 44-45 (according to Ginsberg) maintain that the Seleucids were Babylonian, the head of gold. Ginsberg states that vv 42-43 contradict vv 44-45, unless the interpolator who inserted vv 42-43 "was under the impression that Molon, the revolting satrap of Media, also controlled Babylonia" (page 512). But does Molon ruling Babylonia count as a remnant of the Babylonian empire?