According to 7:22 and 27, the kingdom and the dominion and the greatness of the kingdoms under the whole heaven will be given to the people of the saints of the Most High.
As for the rest of the beasts, their dominion (authority and kingdom) was taken away, but an extension of life (culture) was given to them for a season and for a time (v. 12). This indicates that although the dominion and authority of Babylon, Persia, and Greece were taken away, their life, that is, their culture, will be extended and still remain. Today we are a part of Western culture, the Roman culture. Western culture is the consummation of Roman, Greek, Persian, and Babylonian culture.
Belshazzar, the Babylonian king, was defeated by Darius the Mede. Then Alexander the Great came to defeat Darius the Persian (a different Darius) in 330 B.C. Alexander's four generals succeeded him to rule over four kingdoms. In 27 B.C. Caesar Augustus became the emperor of the Roman Empire, replacing the Grecian Empire. Although the actual Roman Empire came to an end around A.D. 476, the Roman spirit, culture, law, politics, and customs continue to exist. Therefore, in a sense, today we are still a part of the Roman Empire.
The books of Daniel and Revelation unveil God's economy. According to His economy, God will rule over the world, produce a situation for Israel to be His elect, gain the church to be His mysterious people, and have all the nations to be the peoples in the eternal kingdom of God. If we see this, we will know where we are, and we will know the meaning of our human life.