Daniel's vision: the four beasts
Daniel 7 is another vision similar to Daniel 2 about the four kingdoms, which is instead given in terms of beasts:
“Daniel spake and said, I saw in my vision by night, and, behold, the four winds of the heaven strove upon the great sea. And four great beasts came up from the sea, diverse one from another. The first was like a lion, and had eagle's wings: I beheld till the wings thereof were plucked, and it was lifted up from the earth, and made stand upon the feet as a man, and a man's heart was given to it. And behold another beast, a second, like to a bear, and it raised up itself on one side, and it had three ribs in the mouth of it between the teeth of it: and they said thus unto it, Arise, devour much flesh. After this I beheld, and lo another, like a leopard, which had upon the back of it four wings of a fowl; the beast had also four heads; and dominion was given to it. After this I saw in the night visions, and behold a fourth beast, dreadful and terrible, and strong exceedingly; and it had great iron teeth: it devoured and brake in pieces, and stamped the residue with the feet of it: and it was diverse from all the beasts that were before it; and it had ten horns. I considered the horns, and, behold, there came up among them another little horn, before whom there were three of the first horns plucked up by the roots: and, behold, in this horn were eyes like the eyes of man, and a mouth speaking great things. I beheld till the thrones were cast down, and the Ancient of days did sit, whose garment was white as snow, and the hair of his head like the pure wool: his throne was like the fiery flame, and his wheels as burning fire. A fiery stream issued and came forth from before him: thousand thousands ministered unto him, and ten thousand times ten thousand stood before him: the judgment was set, and the books were opened. I beheld then because of the voice of the great words which the horn spake: I beheld even till the beast was slain, and his body destroyed, and given to the burning flame. As concerning the rest of the beasts, they had their dominion taken away: yet their lives were prolonged for a season and time. I saw in the night visions, and, behold, one like the Son of man came with the clouds of heaven, and came to the Ancient of days, and they brought him near before him. And there was given him dominion, and glory, and a kingdom, that all people, nations, and languages, should serve him: his dominion is an everlasting dominion, which shall not pass away, and his kingdom that which shall not be destroyed.”
The vision of the beasts is summarized and explained in Daniel 7:17-18 as well as in Daniel 8:15-27, and thus is understood to represent four world empires: Babylon, Medes/Persia, Greece, and Rome. Please notice that the fourth beast begins at the time of the Roman empire, but the little horn grows to be a great horn, which we see will be destroyed when the Ancient of days shall come (Daniel 7:22), as is also indicated when the stone shall smite the image (Daniel 2:34-35).
One thing worth mentioning is that even though the four kingdoms are distinctly represented by four different world empires, the image still lives completely on today, and the ultimate culmination is the beast in Revelation 13:1-2. Therefore, even though Babylon is not currently a world empire, the effects of Babylon are evident and pervasive throughout the world today, and likewise the Medo-Persian Empire, the Grecian Empire, and the Roman empire. This is all-to-evident if one were to study the history of western civilization, which traces back it's roots to Babylon. The stone represents the Son of man (Daniel 7:13) who will shatter the image and destroy the beast when He comes again to the earth, and will then establish His kingdom on the earth for 1000 years (Revelation 20:6).