Five kingdoms are described.

King Nebuchadnezzar has had a dream in Daniel 2. Daniel, by revelation from God, both tells the king what the dream is, and what it means. Five kingdoms are prophesied to rule.

“31 You, O king, saw, and, behold, a great image. This image, which was mighty, and whose brightness was excellent, stood before you; and the aspect of it was awesome. 32 As for this image, its head was of fine gold, its breast and its arms of silver, its belly and its thighs of brass, 33 its legs of iron, its feet part of iron, and part of clay.”
Dan 2:31-33 WEB

This is summary here, but the first was ancient Babylon ruled by Nebuchadnezzar himself. “ … you are the head of gold.” Dan 2:38 WEB.

This was followed by the Medo-Persian Empire. This is symbolized by breast and arms of silver, Dan 2:32. It was inferior to Babylon, but lasted longer.

Then came the Greeks under Alexander the Great. Alexander is pictured as a large horn in Daniel 8.

“The shaggy goat represents the kingdom of Greece, and the large horn that is between his eyes is the first king.”
Dan 8:21 WEB

Greece of course was to be followed by Rome. Rome is described Daniel 2 as “legs of iron, its feet part of iron, and part of clay.” In Daniel 7 Rome is described as an frightening beast with large iron teeth. Rome did not seduce or make other rich. Rather she, “devoured and broke in pieces, and stamped the residue with its feet,” Dan 7:7 WEB.

“But in the days of those kings …” Dan 2:44

It is clear it is talking about in the days of the Roman Empire, that,

“the God of heaven will set up a kingdom which shall never be destroyed, nor shall the sovereignty of it be left to another people; but it shall break in pieces and consume all these kingdoms, and it shall stand forever.”
Dan 2:44 WEB

Now there was no clear secular successor to Rome.

The successor is the one,

“… that it broke in pieces the iron, the brass, the clay, the silver, and the gold …”
Dan 2:45 WEB

“Cut out without hands” (Dan 2:34) would indicate that it was by no human agency that this kingdom comes into being. Then we look back to see the nature of this kingdom.

“the stone that struck the image became a great MOUNTAIN,”
Dan 2:35 WEB.

This is a religious kingdom which comes. This is the kingdom of heaven which John the Baptist and Jesus announced, and into which God’s people have been transferred, Col 1:13.

It indeed struck “the iron, the clay, the brass, the silver, and the gold, … and the wind carried them away, so that no place was found for them:” Dan 2:35 WEB

“the stone … became a great mountain, and
filled the WHOLE earth.” Dan 2:35

This is still in process. The kingdom has not YET filled the whole earth. But it will. Scripture cannot be broken, Jn 10:35.

WEB is the World English Bible, a copyright free revision
of the original ASV American Standard Version 1901