Dullahans are European monsters known as 'headless knights' or 'headless horsemen' owing to their most obvious trait: their head isn't attached to their necks.
Dullahans are said to be the spirits of people who were decapitated, and wander the land in search for their heads! It's said that until they find their original heads, they'll never be able to rest in peace! In their quests to locate their missing
noggin, the dullahan travels far and wide, often by wagon or horseback, which is why they're often known as the headless knights or horsemen.
While that's more or less true, most of those who've encountered a dullahan note that they DO, in fact, have a head, although they often carry them under their arm rather than on their necks as is 'traditional'. In most creatures the head houses many important organs and senses, and the dullahan is no different! So even a dullahan needs a head. However, since its original one is perpetually lost, it usually takes a loaner.
Other people are usually attached to their heads - save the odd hydra, who's always good for one or two - so the dullahan inevitably has to take the head by force, which has also given them a reputation as bloody harbingers, riding from place to place and usually killing but a single person in the dead of night. After that the dullahan will carry around the stolen head, using it as their own until they lose it, it gets damaged, or it starts to rot away because it lacks the undying magic of the body.