First, we see in Chapter 7 verse 3 that the beasts come out of the sea. The sea represents the people, or nations, of the earth, as explained in Revelation 12 and other chapters of Revelation.
The key to understanding who the four beasts of chapter 7 represent is found in Daniel 8 1. Daniel says the vision he had in chapter 8 was “after that which appeared unto me at the first.” Thus, we can infer that the four beasts in chapter 7 include Medo-Persia and Greece, just as the vision in chapter 8 does. “The first” could also be referring to the vision of chapter 2, which would lend even more credence to the beasts of chapter 7 being Babylon, Medo-Persia, Greece, and Rome.
Concerning the Roman Empire, the prophecy in chapter 7 has two fulfillments. Prophecy often has multiple fulfillments as opposed to just one as many people believe.
The first fulfillment took place many centuries ago and involved the ten nations of the western Roman Empire. Three of the tribes were destroyed and the little horn that came out of that western Roman Empire was the Roman Catholic church.
This leads to the second fulfillment of this prophecy. In this case, the ten horns represent ten world regions the worldly powers that be are planning to divide the world into. The ten world regions, I believe, will be:
North American Union;
Central-South American Union
Northern European Union (as Daniel 2 says the nations of Europe “shall not cleave one to another”);
Russo-Middle Eastern Union
Australian Union (consisting of Australia and New Zealand merged);
Union of Island Nations
Subsequently, three of the regions will be merged with others. From what I’ve heard, I think these will be the Central-South American, Caribbean, and Northern European unions merging with the North American Union.
More information about the division of the world into these regions can be found various places on the internet. Also of course, entities such as the African Union and the Asian Union have been mentioned in the news before, although at this time these unions are just political in nature.
The little horn represents the Vatican, which will control these ten world regions and make war with the saints as verse 21 of chapter 7 says. This of course parallels with Revelation 13.
Verse 25 says, “and he shall speak great words against the Most High and shall wear out the saints of the Most High and think to change times and laws and they shall be given into his hand until a time and times and the dividing of time.”
As anyone who has studied the teachings of the Catholic church is probably aware, Catholicism has spoken very blasphemous things against God. Any student of the history of the Roman Catholic church will also be aware that it has persecuted Christians for many centuries. However, the Catholic church has also thought it had the authority to change God’s times and laws as well. Laws it has changed include removing the second commandment from its version of the ten commandments and the addition of requirements such as confession and other rituals.
The Catholic church has also tried to change times. The Bible would seem to point to Jesus being born in about 2 B.C., based on verses about who was governor when certain things happened. Yet, Catholicism teaches Jesus was born in 1 A.D. and died in AD 33.
As for time, times and the dividing of time, most prophecy scholars agree this signifies a time of three and a half literal years. When this verse is paralleled with a verse that uses the same terminology in Revelation, I believe this phrasing is pointing to a final three and a half year period of time popularly known as the Great Tribulation.
As for chapter 8, we are told right in this chapter of Daniel that the vision concerns Medo-Persia and Greece. It tells of Alexander the Great and the dividing of his empire into four after his death. Verses 9-14 and 23-26 are speaking of Antiachus Epiphanese (or however you spell it) and his persecution of the Jews. His blasphemous actions against God are spoken of in 1 Macabees. The 2300 days represent the literal period of time Antiachus had control of Jerusalem. A man on YouTube named Barton Aaron Porter has a good explanation of this.