The idea that Leviathan and Behemoth are names of real-world natural animals, the crocodile and hippopotamous respectively, goes back to the Renaissance Protestant author Samuel Bochart who proposed these identifications in 1663. Today these naturalizing identifications are generally rejected by biblical scholars, who recognize that the beasts described are fundamentally mythological (see the exhaustive discussion of the evidence in chapter 2 of John Day's God's Conflict With the Dragon and the Sea, 1985, Cambridge University Press). In particular, Leviathan (lwytn) appears in older Ugaritic texts as the seven-headed sea dragon Lotan (= Ladon in Greek mythology?), parallel to Yamm, Rahab, Tiamat, and other serpentine chaos monsters representing the sea (cf. Job 41:18-21, which describes Leviathan breathing out fire and smoke — which accords with the figure of a dragon rather than a crocodile, cf. Psalm 74:14 on Leviathan having multiple heads, and cf. Job 41:31-32 and Psalm 104:25-26 on the Leviathan dwelling in the open sea). The ox-like Behemoth in turn corresponds to Atik, El's calf, and Arsh, the "beloved of El", which are mentioned as slain by the goddess Anat in the same passage that mentions the seven-headed Lotan (KTU 1.3.III.43-44).
The messianic banquet motif involving the carcasses of Leviathan and Behemoth is one example of the Urzeit-Endzeit principle, that the situation at the beginning of the world resumes at end of the world. Leviathan and Behemoth both have primeval connotations (cf. Job 26:12-13, 40:19, Psalm 74:12-15, 89:9-10), with the vanquishing of Rahab and Leviathan in particular being associated with Yahweh's creation of the world and the restraining of the forces of the watery deep (compare Enuma Elish, IV.93-V.62, Rig Veda 1.32.1-8, Job 38:4-11, Psalm 104:5-11, b. Bava Batra 74b). The provision of the body of Leviathan as food represents God's creative act of providing fresh water for animals on land: "You crushed the heads of Leviathan, leaving him for wild animals to eat, you opened the spring and the torrent, you dried up the inexhastible rivers. You made the day and yours is also the night, you established the sun and the moon; it was you who set all the boundaries of the earth and you made both summer and winter" (Psalm 74:12-17). Isaiah 27:1 (which almost verbatim recalls the wording in the Ugaritic description of Lotan) recasts Yahweh's battle against the sea dragon in eschatological terms, and Isaiah 25:6-8 is the passage that started the subsequent messianic banquet tradition in apocalyptic literature (cf. 1 Enoch 60:7-10, 4 Ezra 6:49-52, 2 Baruch 29:4, Midrash Rabbah, Bereshith 11.9).
It is important to recognize that here Leviathan represents the sea and Behemoth represents the land. The Ziz is conspiuously absent in all older biblical and apocalyptic traditions and it is a fairly clear later addition to this underlying scheme; the Ziz fills out the third domain where God's creatures live — the sky. This represents an interpretation of Genesis 1:20 wherein God created on the fifth day creatures in the water and birds flying above the earth in the sky. The name Ziz was taken from Psalm 50:11: "I know every bird in the mountains and the moving creatures (zyz) of the field are mine". The midrash that produced the "Ziz" took zyz (which elsewhere only occurs in the OT at Psalm 80:13) as a name referring to a unique bird monster analoguous to the Leviathan and Behemoth, even tho in its original context kl-zyz referred to a class of moving creatures of the field and was only incidentally mentioned in the same sentence with birds. The character of the Ziz however embodies a mythological concept of a cosmic solar bird (cf. the Garuna of Indian mythology), and there is probably a precedent for it in 3 Baruch which draws on both Egyptian phoenix and Byzantine griffin traditions (ch. 6-8).
