"'And there before me was a second beast, which looked like a bear. It was raised up on one of its sides, and it had three ribs in its mouth between its teeth. It was told, "Get up and eat your fill of flesh!"'" NIV translation
This second beast corresponds to the chest and arms of silver of the statue in Nebuchadnezzar's dream. This is the Media-Persian empire led by Xerxes which conquered the Babylonians. The three ribs in the bear's mouth speaks of their conquest of Babylon, Lydia, and Egypt. We notice that it was told to eat its fill which reminds us that it was God who had used them as an instrument of judgment on the Babylonians.
"'After that, I looked, and there before me was another beast, one that looked like a leopard. And on its back it had four wings like those of a bird. This beast had four heads, and it was given authority to rule.'" NIV translation
This third beast corresponds to the belly and thighs of bronze in Nebuchadnezzar's dream. Once again, this is the Greco-Macedonian empire led by Alexander the Great. The speed of his army and their conquest was unmatched and so we see that they had four wings (more than the wings of the first beast). The four heads speaks of the fact that when Alexander died (at the early age of just 33), his four generals divided up his vast empire.
"'After that, in my vision at night I looked, and there before me was a fourth beast - terrifying and frightening and very powerful. It had large iron teeth; it crushed and devoured its victims and trampled underfoot whatever was left. It was different from all the former beasts, and it had ten horns.'" NIV translation
Daniel's second vision of the night is of a beast like none he had ever seen before. The iron teeth refer to its strength and also reminds us of the legs in the statue of Nebuchadnezzar's dream. The ten horns are the ten toes of the feet of Nebuchadnezzar's statue and the fact that they are mixed with clay brings to mind weakness. This beast is the Roman empire.
"'While I was thinking about the horns, there before me was another horn, a little one, which came up among them; and three of the first horns were uprooted before it. This horn had eyes like the eyes of man and a mouth that spoke boastfully.'" NIV translation
Unlike the other three beasts (empires) the Roman empire was never conquered but instead just faded away into history. As we see here, three parts of what was the Roman Empire will be reunited under the leadership of this other part. This horn is the beast that John spoke of coming out of the sea (nations) in Revelation 13.