Wikipedia gives a pretty good summary of Revelation beasts.
It names the beast from the sea (ch 13), the scarlet beast (ch 17), the beast from the earth (13:11-18).
There is also the dragon identified as Satan (Ch 12, 16:13, 20:2). The beasts found in the seals and throne sections (ch 4,5,6, 7:11, 14:3, 15:7, 19:4) are a different Greek word, zoon as opposed to Therion. These beasts are like cherubims and Seraphim found in various books of the Bible (Eze Ch 1, ch 10, Isa ch 6). They bear resemblances to other middle-eastern composite beasts such as sphinxes, lamassu, and genii. The middle-eastern creatures are related to seasons and zodiacal signs. In Revelation, they are associated with the throne of God and the four horsemen (ch 6).
Wikipedia lists four modern interpretations of the later beasts (ch 13-19).
Preterism - Most often the first beast is Nero and the second is the imperial cult.
Historicism - Favored by the Reformers. The beast and false prophet were most commonly identified with the papacy in its political and religious aspects.
Idealism - The beast from the sea is interpreted as the state or any human kingdom that is in opposition to God. This would include the Roman Empire but would broadly apply to all empires. Scholars take their cue from the parallels between Revelation 13 and Daniel 7, noting that in Daniel 7:17 that the beasts are revealed as kingdoms.
Futurism - Futurism often interprets the beast from the sea to represent a revived Roman empire that will oppose Christians in the last days.
Relation to Daniel
As noted, these beasts are similar to the beasts found in Daniel where they are usually interpreted as Babylon, Medo-Persia, Greek Empire, and the Roman Empire. However, the church historian Eusebius gives us an alternate interpretation of Daniel.
For it was quite consistent in the king, whose view of the spectacle of life was so false, and who admired the beauty of the mere sensible colours, so to speak, in the picture set up to view, to liken the life of all men to a great image; but (it became) the prophet to compare the great and mighty tumult of life to a mighty sea. And it was fitting that the king, who prized the substances deemed precious among men, gold, and silver, and brass, and iron, should liken to these substances the kingdoms that held the sovereignty at different times in the life of men; but that the prophet should describe these same kingdoms under the likeness of beasts, in accordance with the manner of their rule. And again, the king—who was puffed up, as it seems, in his own conceit, and plumed himself on the power of his ancestors—is shown the vicissitude to which affairs are subject, and the end destined for all the kingdoms of earth, with the view of teaching him to lay aside his pride in himself, and understand that there is nothing stable among men, but only that which is the appointed end of all things—the kingdom of God."
Scholia on Daniel
In comparing the vision of chapter 2 to the vision in 7, Eusebius sees the differences as different views of how the king and prophet consider the lives of all men. This is perhaps similar to the way the Greek poet Hesiod describes his ages of man. Hesiod describes the five Ages of Man.
Golden Age - Men had a youthful appearance and eventually died peacefully.
Silver Age - They lived only a short time as grown adults, and spent that time in strife with one another.
Bronze Age – Men of the Bronze Age were hardened and tough, as war was their purpose and passion.
Heroic Age – The Heroic Age is the one age that does not correspond with any metal. It is also the only age that improves upon the age it follows.
Iron Age – During this age humans live an existence of toil and misery.
There seems to be a correspondence to the ages of man and the physical aging of a natural person, with the Heroic age representing intellectual wisdom while the body weakens, and eventually, dies.
Another early Christian apocalypse is the Shepherd of Hermas, which seems to bring together the parables of Jesus with the symbolism of the Apocalypse. Hermas sees a tribulation beast with four colors that are reminiscent of the beasts in Revelation. Instead of multiple heads and horns, Hermas is told of commandments and similitudes.
Although Hermas doesn't mention 7 and 10, other church fathers associated these numbers with the spirit and the law.
- For if we determine on the number that should indicate the law, what else can it be but ten? For we have absolute certainty that the Decalogue of the law, that is, those ten well-known precepts, were first written by the finger of God on two tables of stone. (Deut. ix. 10.) But the law, when it is not aided by grace, maketh transgressors, and is only in the letter, on account of which the apostle specially declared, “The letter killeth, but the spirit giveth life.” (2 Cor. iii. 6.) Let the spirit then be added to the letter, lest the letter kill him whom the spirit maketh not alive, and let us work out the precepts of the law, not in our own strength, but by the grace of the Saviour. But when grace is added to the law, that is, the spirit to the letter, there is, in a kind of way, added to ten the number of seven. For this number, namely seven, is testified by the documents of holy writ given us for perusal, to signify the Holy Spirit. For example, sanctity or sanctification properly pertains to the Holy Spirit, whence, as the Father is a spirit, and the Son a spirit, because God is a spirit, so the Father is holy and the Son holy, yet the Spirit of both is called peculiarly by the name of the Holy Spirit. Where, then, was there the first distinct mention of sanctification in the law but on the seventh day? "
NPNF1-07. St. Augustine: Lectures or Tracates on the Gospel according to St. John; Tractate CXXII, Chapter XX. 30-31, and XXI. 1-11.
...The number ten signifies the Decalogue, and one hundred shows the crown of virginity.
For he who has preserved entire his resolution for virginity, and faithfully fulfilled the precepts of the Decalogue, and has overcome impure actions and impure thoughts among the chambers of the heart so that they do not rule him, this is truly a priest of Christ and entirely completes the millenary number, believed to rule with Christ, and rightly with Him the devil is bound...
Jerome (ending to his version of Victorinus' commentary, which replaces Victorinus' material on chapters 20 and 21 of the Apocalypse)
Therefore, taking to you a masculine and sober mind, oppose your armour to the swelling beast, and do not at all give way, nor be troubled because of his fury. For you will have immense glory if you overcome him, and take away the seven crowns which are upon him, on account of which we have to struggle and wrestle, according to our teacher Paul. For she who having first overcome the devil, and destroyed his seven heads, becomes possessed of the seven crowns of virtue, having gone through the seven great struggles of chastity. For incontinence and luxury is a head of the dragon; and whoever bruises this is wreathed with the crown of temperance. Cowardice and weakness is also a head; and he who treads upon this carries off the crown of martyrdom. Unbelief and folly, and other similar fruits of wickedness, is another head; and he who has overcome these and destroyed them carries off the honours connected with them, the power of the dragon being in many ways rooted up. Moreover, the ten horns and stings which he was said to have upon his heads are the ten opposites, O virgins, to the Decalogue, by which he was accustomed to gore and cast down the souls of many imagining and contriving things in opposition to the law, “Thou shalt love the Lord thy God,” (Deut. vi. 5.) and to the other precepts which follow.
Methodius, Symposium, Thekla, Chapter XIII.—The Seven Crowns of the Beast to Be Taken Away by Victorious Chastity; The Ten Crowns of the Dragon, the Vices Opposed to the Decalogue; The Opinion of Fate the Greatest Evil.
I call this the "Wisdom" interpretation of Revelation. The Greeks loved wisdom (1Co 1:22). After all, Revelation calls for wisdom to understand the beast (13:18, 17:9).
2Pe 2:12 But these, as natural brute beasts, made to be taken and destroyed, speak evil of the things that they understand not; and shall utterly perish in their own corruption;