To start with, a drakon is a snake. The Greeks used the word to refer to both huge monsters and mundane snakes. Drakon itself is derived from the word dérkomai and is believed to literally mean, "the one who sees". The hypnotizing power attributed to snakes is present in drakons, traditionally given the job of the sleepless guardian of treasure. Going back even further, we see that the drakon comes from two disparate cultural perceptions of snake, each of which is still present in its classical form.

Snake Goddess - One of the native precursors of the Greeks were the Minoans. They had more in common with their Egyptian and Near Eastern neighbors than the Italians and Balkans. From what little we can gather of their culture, it appears the snake was a symbol of the goddess. Whether or not it was any goddess in particular is unknown. This theme survives into ancient Greece, however. Athena often uses snakes as agents when acting with mortals, Hera uses them as well (the twin serpents who attempted to strangle Heracles and the Hydra), and Medea had a chariot pulled by snakes. Earth goddesses in particular are heavily associated with them. Python was a direct product of Gaia, and the snake was a divine symbol of Demeter, who also had a rad snake chariot. Even in mortal women, their dynamic with snakes and dragons is nurturing. Several heroines sing to snakes as their masculine counterparts steal the treasure they guard, fulfilling a nurturing role in comparison to the destructive masculine one. Here the snake is a guardian, a creature of the earth and everything beneath it, including gold and the dead. These dragons are usually not slain, but pacified by the presence of a woman. In addition, the beard is an originally Greek symbol associated with snakes, particularly those connected to the gods. This was quite possibly a signifier of their supernatural status above mundane serpents. The goddess depicted above isn't any one in particular, though her dress does pull from a statue of Athena holding a curled python.

Drakaina - One way in which the snake goddess has survived is in the drakaina. This word is simply the feminine form of drakon, but also encompasses the numerous beings characterized by having the upper body of a woman and the lower body of a drakon. Numerous beings in Greek mythology fit this theme, but the one I've focused on is the Scythian drakaina, a woman who intercepts Heracles during one of his labors and kidnaps some cows. She offers to return the cattle in exchange for a night of intercourse. And then Herc is off and we're told the three sons of that union go on to become kings of great renown in Scythia. Some authors interpret this as a Greek adaptation of a Scythian myth, with one of the key pieces of evidence being that the drakaina's name is Hora, meaning "Seasons". Regardless of whether or not this is a goddess, it is a story where the snake-woman is neither killed nor stolen from, instead given the prestige of being the founder of a line of kings.

PIE Chaos Serpent - From the Proto-Indo-Europeans up North, we get the dragon we're all more familiar with. Serpents of this breed, such as Apep, Tiamat, and Jormungand, are all enormous, destructive creatures allied with darkness and the unforgiving seas. They represent the primordial chaos from what order sprang out of, and often have a hand in trying to return the world to that way. One of the primary themes associated with them is the dragon slayer: a god or hero who fights a dragon to save something, be it a land or treasure or an Ethiopian princess.

Typhoeus - This guy, though significantly more humanoid and giant-like than any others, is the clearest example of a PIE chaos serpent in Greece. It does not get more typical than a giant snake (like) monster fighting a storm god. Typhoeus probably sprung from traditions where he was more serpentine, but gradually added other aspects. Such as his own storm god qualities. In Greece, gods associated with the winds are always given wings, save for Zeus. The two's battle is reflective of a battle between the terrible whirlwinds and lightning strikes and the calmer, helpful rain showers that enable humanity to survive. 

And then we get to the drakon proper. Taking elements from both sides of the tree, the archetypal Greek drakon is an enormous, often monstrous serpent associated with both the underground and the waters in some way. They are agents of gods, most often goddesses, sent to battle heroes or guard priceless treasures. Sometimes they're killed, sometimes they're merely lulled to sleep by a helpful maiden. Rather than breathing fire (which everything from mechanical bulls to horses to giants do), they possess venoms and rows of sharp teeth. Mention of their terrible gazes is often made. This drakon has both a beard and a casque-like crown, common elements in drakon descriptions from Greece. Its face is much less serpentine, being modeled after a clay illustration of the Colchian dragon. This gives is a suitably monstrous look, as if it were being pealed from layers of mud.

Chimera - Despite its odd appearance, the chimera fits the pattern of a dragon terrorizing a countryside and being slain by a plucky hero. The chimera may in fact be the originator of the classical Saint George imagery, where the saint is depicted as towering over a crawling, pitiful dragon. A 3rd century mosaic from Imperial Rome may have started this trend. What makes her (because despite her mane the Chimera is a female) stand apart from all the rest is the sheer strangeness of her form compared to others. Especially the little goat that comes out of her back, like a rider. Which I had to cut for spacing reasons :(

Hydra - Another classical Greek dragon is the multi-headed hydra, who has given its name to a whole genre of creatures with more heads than they ought to have. In addition to having the attributes of a typical Greek drakon, the Hydra has two traits seen in Mesopotamian monsters as well. The first is the amount of heads. Having many heads is not as common in Greece as it is in the Near East, where the idea of an eleven-headed sea serpent pops up numerous times across several different cultures. The second is that the hydra, in its earliest mentioning by Hesiod, is said to have been raised by Hera specifically to combat Heracles. This same tactic is done by a few Mesopotamian gods. In their realm of influence, monsters are pawns of the gods, who send them out to do their bidding on Earth while they lounge in Heaven. Our Hydra may have been a later influence from Greece's neighbors to the East. Also, had to add in the crab that Hera also sends in to help the hydra. If this were a spec bio piece, I would make it a species of crab that evolved to clean the hydra of parasites.

Cetus - Sea monsters such as these are perhaps the furthest from the traditional Greek drakon, while still remaining core parts of the mythology. In form cetoi range from exaggerations of real whales and sharks to dog-headed serpents with frilly fins and ears. Or even animal-headed fish. Because they live underwater, they almost always function as tools of divine vengeance. Kinda hard to steal treasure underwater. Heavy metal tends to sink. While cetus was originally a word for any sea monster, it would eventually become the root of the scientific term cetacean: whales and dolphins.

But the tree doesn't end there. See, even after the culture we recognize as the Ancient Greeks and Romans faded, their dragons still lived on. Medieval Europe, with its glorification of Greco-Roman texts, derived many of their folk beliefs from their predecessors. Or, the people who they liked to imagine were there predecessors.

Draco - The Romans adopted the Greek drakon whole-clothe, like a lot of stuff. The only noteworthy original dragon to come out of the pre-Fall Roman era was the Dacian Draco. The Dacians used the image of a dragon as a standard during war-time, represented as a serpent with the head of a dog. When conquered, the Romans adopted this, possibly beginning the Western tradition of associating dragons with military power and identity. The dog-headed serpent would also survive to the modern period, showing up in descriptions of Balkan lamya. 

Indian Drakon - Here begins a tradition in Greek and Roman literature that claimed that foreign parts were full of large, dangerous, and more interesting fauna than the mundane peninsula they were all stuck on. This is a common theme of humanity in general, where everyone you're not familiar with is teeming with exciting and ancient life. Just look at cryptozoology. India in particular was a favorite of Greek tall tales, being far away for journeys to be rare, but also rich and full of exotic animals. Philostratus populated India with three types of drakons: the lowly marsh, the silver hill, and the dazzling golden mountain drakons. They were typical in every respect, having enormous sizes, red crowns, beards, and guarding treasure beneath the earth. An interesting addition was that they were the mortal enemies of elephants. Being the largest land-animal (in real life), they made perfect prey for these humongous serpents. Feeding on them was fraught with peril, however, as the struggle between reptile and mammal could result in the death of either party, or both. To symbolize the foreignness of the drakon, I drew it as a sort of hybrid between the drakon and the Hindu naga. 

Pliny's Drakon - This drakon is otherwise the same as the Indian, but is the start of another theme. As time went on, philosophers began taking more grounded looks at fantastical animals. While also perpetuating even more outrageous falsehoods. None was more popular than Pliny the Elder, hence the name. He believed that, while foreign drakons might be real, they were much more similar to the snakes of Greece than the monsters of legend. He scoffed at the crowns and hair they were adorned with. His Natural History was the first of many instances where the fantastical elements of the dragon were toned down to seem more palatable to a scientifically minded audience. It also introduced an interest into the life history of the dragons, treating them as real animals with lives beyond the myths. Our dragon up top evolved to resemble pythons, rather than the other way around to what probably happened in real life, where pythons were exaggerated to become dragons.

Then, we get two foreign influences, which would come to shape the modern definition of the European dragon. Christianity's influence cannot be understated here. As Jonathan Evans states in Medieval Folklore, the dragon came to be confused with several other desert animals. In Jewish and early Christian belief, desert animals were themselves demonic, living in inhospitable regions devoid of human life. Later, texts like Revelations would specifically denote dragons as heralds of evil, and even harbingers of Armageddon itself. This is in contrast to the morally neutral Leviathan. In the medieval era, dragons were beings of evil, without a doubt. Bestiaries were full of on the nose fables about how the natural lives of dragons. Like how they could not stand the breath of a panther (a symbol of Jesus Christ). Or how they could not catch birds that nested in the Peridexion tree (the tree being the church and the birds being Christians, who are safe from the devil so long as they do not stray from the arms of God). This is represented by a typical medieval devil, being brightly colorful and made in mockery of God's creations, aka a weird hybrid with a snake coming out of his butt. Then, the Germanic dragon. This is seen especially in Northern and Western Europe. The Germanic dragon is otherwise similar to the Greek, except that it began as a character of evil. Lindworms and other serpents are almost always antagonists, and there is no heroine who saves them from their fate of death. They also had a stronger connection to treasure. Greek dragons guarded treasure as a job, but the very existence of Germanic dragons is tied with their golden hoards. In addition, in Greek myths, getting transformed into an animal is usually the end of one's story. With the Germanic dragon, it's merely the beginning. Transformed dragons act as antagonists and moral lessons wrapped in one; a lesson to all to not be greedy. Germanic dragons, represented by the lindworm, reinforced their role as antagonists and agents of selfish evil.