Dragons feature prominently in medieval art. Did people believe they were depictions of real creatures or were they interpreted as allegories? Did scholars believe in their existence or was there a difference between the beliefs of ordinary people and educated people? Edit: I’m thinking about European medieval people here.
Yep, they sure did. Dragons are mentioned in medieval bestiaries, which were essentially natural encyclopedias of animals from around the world. The dragon is frequently featured there, and is described typically as a large serpent which frequently preys on elephants. The Medieval writers who wrote about them largely inherited descriptions of them from Classical writers. Here is a description of a dragon from Pliny the Elder's Natural History:
India [...] produces [...] the dragon, which is perpetually at war with the elephant, and is itself of so enormous a size, as easily to envelope the elephants with its folds, and encircle them in its coils. The contest is equally fatal to both; the elephant, vanquished, falls to the earth, and by its weight, crushes the dragon which is entwined around it.
Now here is a description from a Medieval English monk Bartholomaeus Anglicus, in his own work On the Properties of Things:
Between elephants and dragons is everlasting fighting, for the dragon with his tail binds and spans the elephant, and the elephant with his foot and with his nose throws down the dragon, and the dragon binds and spans the elephant’s legs, and makes him fall, but the dragon takes it full sore: for while he slays the elephant, the elephant falls upon him and slays him too. Also the elephant seeing the dragon upon a tree, goes him to break the tree to smite the dragon, and the dragon leaps upon the elephant, to bite him between the nostrils, and attacks the elephant’s eyes, and sometimes blind him, and sometimes leaps upon him from behind, and bites him and sucks his blood. And at last after long fighting the elephant becomes feeble for great blindness, in so much that he falls upon the dragon, and slays in his dying the dragon that killed him.
The cause why the dragon desires his blood, is coldness of the elephant’s blood, by the which the dragon desires to cool himself. Jerome says, that the dragon is a full thirsty beast, insomuch that he may have water enough to quench his great thirst; and opens his mouth against the wind, to quench the burning of his thirst in this way. Therefore when he sees ships sail in the sea in great wind, he flies against the sail to take their cold wind, and sometimes overthrows the ship because of the greatness of its body, and the strong force against the sail. And when the sailors see the dragon coming, and know his coming by the water that swells against him, they strike the sail at once, and escape in this way.
As you can see, it owes a lot to Pliny.
Now, as far as allegory goes, most if not all animals in medieval bestiaries were interpreted allegorically as well as morally. This is based on the logic that if God created heaven and earth, he would leave a sort of 'natural Bible' in nature itself, for people to learn of Him through it. Dragons were no exception to this rule, and were often interpreted as symbols of Satan. This is based on the Bible (for e.g in descriptions of Satan as the red dragon in Revelation). Certainly the popular depiction in medieval art of a saint triumphing over a dragon or serpents is influenced by this. As a few examples, St. Michael and St. George are famous medieval dragon-slayers, while St. Margaret is said to have emerged unscathed from a dragon's belly after it swallowed her.
As an example of a depiction of Satan as a dragon, here is a 15th century depiction of the scene from Revelation of the Red Dragon handing his sceptre to the Beast from the Sea:
http://www.artsycraftsy.com/art/dragons/apocalypse_dragon.jpg
So the dragon was thought of as a real animal, but like other real animals was used frequently in art and literature to represent evil and the Devil.
(Source: Medieval lore : an epitome of the science, geography, animal and plant folk-lore and myth of the middle age: being classified gleanings from the encyclopaedia of Bartholomew Anglicus on the properties of things [in J.Trevisa's translation] - this contains Bartholomaeus Anglicus' description of the dragon, mentioned above, and can be found online).
I assume you're asking about European beliefs?
What did people in, say, China around this timeframe believe, seeing as the dragon is even in the Chinese zodiac?
