Etymology: Kansai どや ("How about that?", the regional equivalent of どうだ) + 顔 (face), with the compound reading がお. It names the face someone makes at the moment of showing off. The どや part is written in katakana even though it is not a loanword - the katakana marks it as slangy.
Register: Casual slang, at home online and in youth speech since roughly the late 2000s. Avoid it in writing for work or school.
Nuance: Usually teasing rather than hostile. Calling someone's expression a ドヤ顔 pokes fun at the self-satisfaction while often conceding they did well. It is also affectionately used of pets - a cat sitting proudly is a stock example - and of oneself, in self-deprecating jokes.
Common patterns
- ドヤ顔をする / している - to make (or be wearing) a smug face; the を is often dropped in speech
- ドヤ顔で〜する - to do something with a smug expression
Similar words
- 得意顔 - a proud or triumphant look; the standard, neutral word, usable in writing
- 自慢 - boasting; the act of showing off rather than the face
- 勝ち誇った顔 - a triumphant face, after actually winning something
The slang ドヤ顔 differs from 得意顔 mainly in tone: it always carries a note of "and it's a bit much".