Laying the Foundation

In Daniel 7 we find Daniel has a vision of four beasts. A lion, a bear, a leopard and a dreadful and terrible beast with ten horns. Then a little horn comes up among the ten horns and plucks up three by the roots.

    A beast represents a kingdom (Daniel 7:23).
    Horns on a beast represent kings/kingdoms that arise out of said beast/kingdom (Daniel 7:24).

Knowing this, we can interpret that the four beasts Daniel sees are four kingdoms, which are described as coming up one after another.

The beasts described in Daniel's vision:

NOTE: Links below are to Bible Hub commentaries on the verses and the identified kingdoms.

    Lion (Babylon; Daniel 7:4)
    Bear (Medo-Persia; Daniel 7:5)
    Leopard (Grecia; Daniel 7:6)
    Dreadful and Terrible (Rome; Daniel 7:7) with Ten horns (divided Rome; Daniel 7:7)
    Little horn (Daniel 7:8)

The fourth kingdom being Rome, history records that it divided into ten kingdoms.

Seven of the divided kingdoms of Rome survive today in Europe.

    Alemanni -> Germany
    Anglo-Saxons -> England
    Burgundians -> Switzerland
    Franks -> France
    Lombards -> Italy
    Suevi -> Portugal
    Visigoths -> Spain

Daniel 7:9 describes the little horn as coming up among the ten kingdoms of divided Rome and plucking up of three of the ten kingdoms by the roots, leaving seven (above).

    Vandals -> No longer exists
    Heruli -> No longer exists
    Ostrogoths -> No longer exists

Summary:

    The Daniel 7 prophecy points to four kingdoms coming up one after another, starting with the literal Babylon.
    In the subsequent kingdoms we can see a lineage that begins with Babylon and ends with the little horn as the primary focus.

Revelation 13 picks up where Daniel leaves off.

Bringing in Revelation 13

In Revelation 13, John describes two beasts. We will only cover the first beast in this post.

A beast rises out of the sea.

    Revelation 13:2 And the beast which I saw was like unto a leopard, and his feet were as the feet of a bear, and his mouth as the mouth of a lion: and the dragon gave him his power, and his seat, and great authority.

    This is a singular kingdom.
    It has attributes of the kingdoms of Daniel 7!
        Like a leopard (Grecia).
        Feet of a bear (Medo-Persia).
        Mouth of a lion (Babylon).
    The dragon (Satan; Revelation 12:9; 20:2) gave him his power, and his seat, and great authority

In these attributes we can see the lineage of this sea beast originates in Babylon. It retains attributes from each kingdom.

What kingdom was the last one mentioned in Daniel 7? The little horn.

Daniel 7:9-11 describes the horn as being judged and destroyed.

    Daniel 7:9-11 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.

We know then that the little horn persists until the end of time and is a key player in end time prophecy.

Revelation 17 gives more detail concerning Babylon. It describes a woman (a symbol for a church; Jeremiah 6:2, 2 Corinthians 11:2, Revelation 19:7-8) on a scarlet beast (kingdom) with the name Mystery, Babylon The Great, The Mother Of Harlots And Abominations Of The Earth, written on her forehead.

    Revelation 17:3-5 So he carried me away in the spirit into the wilderness: and I saw a woman sit upon a scarlet coloured beast, full of names of blasphemy, having seven heads and ten horns. And the woman was arrayed in purple and scarlet colour, and decked with gold and precious stones and pearls, having a golden cup in her hand full of abominations and filthiness of her fornication: And upon her forehead was a name written, Mystery, Babylon The Great, The Mother Of Harlots And Abominations Of The Earth.

This is spiritual Babylon, the very same little horn power that came up among the ten divided kingdoms of Rome and plucked up three from the roots, It came to power and spoke blasphemy against God, thought to change God's times and laws, and persecuted the saints for a 1260 year period (Daniel 7:25).

This same power, the sea beast, according to Revelation 13, would receive a deadly wound that would later be healed. The little horn received its deadly wound at the end of the 1260 year period, but its deadly wound has been healing since.

Literal Babylon is the literal kingdom that existed but is long since destroyed. Spiritual Babylon (aka Mystery Babylon) is a subsequent kingdom comprised of attributes going back to literal Babylon. It came out of Babylon, Medo-Persia, Grecia and Rome. Thus is the lineage shown.

Identifying the Little Horn aka Mystery Babylon

What was literal Babylon know for? Idolatry and forced worship on pain of death (Daniel 3).

What will be instituted in the last days by Mystery Babylon? Idolatry and forced worship on pain of death (Revelation 13:15-17).

Looking back to the quoted Revelation 17:3-5 (above), what colors does the woman (church) wear? Purple and scarlet.

What else is described about the church? She is decked in precious stones and pearls, and has a golden cup in her hand full of abominations and filthiness of her fornication.

You should have enough information to identify who Babylon is.