Dragon
Dragons are mythical creatures found all around the world, possibly inspired by various sources such as giant lizards and snakes, but also dinosaur bones and simple tall-tales from travelers in distant lands. Dragons are often keepers of treasure that they can breathe fire or poison.
Because of their majestic, fantastic nature, Dragons are a staple of much fantasy fiction and games. One of the most well known dragons is Smaug, from Tolkien's The Hobbit. The vast majority of later portrayals of dragons in fiction was based on Smaug, who in turn had been inspired by the dragon Fafnir, from the Völsunga Saga and the dragon from Beowulf.
Dragons are one of the main selling points of the Dungeons & Dragons game, to the point that the 4th edition includes a draconian race called Dragonborn, intended for players who "want to look like a dragon".
Dragon kind and Half-Dragons are basically the confirmation of the rule that dragons can mate with anything, just like humans, fiends, celestials, slaadi, mordons/inevitables/formians, and gribbly abominations from the far realm. We now permit you to take a break to use the brain oxi-clean provided to you by Billy May's ghost to scrub any mental images you may have of a human, dragon, angel, balor, black slaad, formian queen or-OH SWEET MERCIFUL GOD-EMPEROR THE MENTAL IMAGE!!!!
There are also 'Dragon Riders' (and that's literal riders, in case you didn't use enough brain bleach just 5 nanoseconds ago) but they're really just pussy knights that just pilot the Dragons and let them fight for them, occasionally dismounting to deliver a finishing blow or give a pompous bullshit speech. (Except for Viking Dragon Riders, hardcore shit right there)
Johnniass Dragonraper is known to rape a dragon on occasion.
Toothless Dragon the Dawww-est dragon.
Warhammer
Dragons have appeared since the beginning in Warhammer Fantasy, but they're one of the most vaguely defined parts of the lore. They will ally themselves with the High Elves and be used as powerful, and in game terms, expensive, mounts for elven lords. Aside from being intelligent, there's not much stated about them. Some dragons have also been corrupted by Chaos and fight alongside the Warriors of Chaos. In both cases, they are made out to be among the most powerful monsters in the setting, and their stats live up to it, with only few models, including Greater Daemons, having a chance at beating them.
Storm of Magic introduce "Emperor dragons", huge dragons that are arguably the most powerful units in the book. Emperor dragons not allied with Chaos can also be upgraded all the way up to level four sorcerers, in addition to having nearly all 9s across their statline.