D&D Monsters: Stirges

The strige is a creature of Roman myth, derived from the earlier Greek strix. It was said to be a nocturnal bird, albeit one that hung upside down like a bat, which drank the blood of infants and possibly even ate the remains. The Greek version of the name has since been adopted as a scientific name for a genus of owl, and, blood-drinking aside, the general description does seem to match owls more than anything else that might exist in the real world. The name later also became associated with witches and with a more humanoid form of vampire, the strigoi. 

In D&D, of course, the name mutates again to the form "stirge". While it looks even less owl-like than the mythic creature, it's still clearly based on it... but is more inclined to attack adults than babies.

D&D Monsters: Manticores

Manticores are creature not of Greek, but of Persian, myth. The name literally means "man-eater", and it's at least possible that it originated with a "traveller's tale" style exaggeration of man-eating tigers. They were supposed to be hungry for human flesh - something retained in D&D - and were often described as having a "scorpion-like" tail, although most historical illustrations show a cluster of spikes on the end of the tail instead.

When the creature was adopted for D&D, however, Gygax made a major innovation to the mythic creature: he gave it wings. (At least, this is true by the 1E Monster Manual; the original version of the rules apparently doesn't mention the feature). Although this is original to the game, it has become a common trope of manticore pictures since, even outside of D&D, although it's far from universal.

D&D Monsters: Griffons and Hippogriffs

The mythic origins of griffons lie in Ancient Greece, if not earlier - a combination of the king of the beasts and the king of the birds. The specific form of that combination was largely cemented by the late Middle Ages into the one we are currently familiar with, and griffons ('griffin' and 'gryphon' are equally valid spellings) are common features in modern fantasy, especially in RPGs. 

The hippogriff, however, is much more modern; it first appears in a poetic work of fiction written in 1516, where it is described as the offspring of a male griffon and a female horse (which, since griffons were thought to kill and eat horses on sight was intended as something miraculous). Although the existence of one may well imply the other, it's possibly more common than the griffon itself in fantasy fiction, with the most famous modern example being that in the Harry Potter books.

D&D Monsters: Mummies

The concept of the mummy as an undead monster is really a 20th-century invention, beginning with the 1932 horror movie The Mummy. While mummies and immortal Ancient Egyptians had featured in earlier fiction, they were not really in the form we're familiar with now, or that formed the basis for the D&D monster, and still don't date back any further than the mid-19th century. Since their 1932 debut, however, they have appeared in a number of older-style horror films, and become something of a cliche, if not quite as popular as werewolves and vampires.

In D&D, they are mid-powered undead, falling into what I've termed the "wilful corporeal" category, given that they retain sentience and intelligence alongside their physical body. Under that scheme, they would fall somewhere between a wight and vampire in terms of power, but they are quite different from both. The look of a mummy does not, of course, change notably between editions; they are bandage-wrapped mummified corpses, sometimes dressed in funereal finery, but more usually not. Like most D&D undead (except vampires) depictions of females are rare, although not quite to the extent that is true of, say, ghouls or wights.

D&D Monsters: Giant and Phase Spiders

The first edition of AD&D includes a number of giant invertebrates, mostly insects. The idea behind these may be influenced by the "big bug" films of the post-WWII era, starting with Them! in 1954, and they provide the possibility of exotic-looking monsters that nonetheless have to look no further than the natural world for inspiration. 

Once we leave insects and look at spiders, there is an even more obvious inspiration: Shelob in Lord of the Rings. While she, and her relatives in other Tolkien works, were likely the primary inspiration behind the original giant spiders of D&D, there are plenty of other fictional examples. The cinematic classic The Giant Spider Invasion is one such (yes, I've actually seen it; there's 80+ minutes of my life I'm not getting back...) and, from more modern fiction, there's Aragog in the Harry Potter books. Giant spiders aren't found in European myth, but there are the Tsuchi-gumo of Japan, which are usually described as spiders (but sometimes crickets) and, at a stretch, Anansi the spider-god of West Africa.

D&D Monsters: Unicorns

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Unicorns are probably one of the best-known mythological creatures of medieval Europe, perhaps on a par even with dragons. Their origins are likely earlier than this, with the general concept of "one-horned magical beast" going back to at least the Ancient Greeks and having counterparts in other cultures, too. Some of these were aggressively dangerous, but it's the medieval version, appearing in religious bestiaries as an object lesson in virtuous purity that we're most familiar with and that forms the basis of the D&D creature. 

So iconic is the appearance of the unicorn that it's one of the few creatures in D&D that looks pretty much the same in every edition, regardless of artist, and that closely follows its traditional form. Early medieval unicorns weren't necessarily white, and some looked more like a goat than a horse, but such variations have long since vanished from the public mind. Pretty much everyone knows what a unicorn is, and what it looks like.

D&D Monsters: Doppelgangers

Doppelgangers are one of those races that, were they really to exist, would surely have a significant effect on the world and be much on the minds of the general public. That they aren't in the standard D&D universes is largely thanks to the great number of other sentient races that exist, many of which are even more threatening.

The word "doppelganger", which means something like "double-walker" in German, only dates back to the late 18th century. However, the general concept of a spooky double of a person is a common one in mythology, folk tales, and just plain ghost stories going back for thousands of years. It's also a common theme in more recent fiction, with perhaps the alien in the 1938 novella Who Goes There? being a particular inspiration for the D&D version. (The story was later remade as a film titled The Thing, although the black-and-white version Gygax would have been familiar with at the time features quite a different sort of monster).