gesugao

In Japanese, gesugao ゲス顔 means "scum face." In anime, it normally refers to the twisted, grinning expressions characters that are scum, vulgar lowlifes, make when they're enjoying a situation. Savoring the fact they won, often mocking the loser. Or are scheming some evil plan. Or even just throwing slurs at someone they hate.

Generally, gesugao is depicted with the following features:

Looking down at the "loser."
Grinning, laughing, or putting their tongue out mockingly.
One eye slight closed.
Pupils drawn smaller than usual.
Shadow drawn around the forehead.

Anime: Kakegurui 賭ケグルイ (Episode 1)

Examples of gesugao

A lot of western fans mistakenly associate gesugao with girls that are either yandere or "sadist," do-S ド, evil villains with God complexes that think other people are insects compared to them, and scheming bullies or cheaters getting high on the thought of crushing their victims.

Anime: Sword Art Online: Alicization (Episode 23)

You can tell by the fact that you can see Quinella's molars at the ceiling of her mouth that she is, indubitably, looking down at you.

Male Gesugao

However, the term actually applies to either gender, and you're more likely to see an evil dude with a gesugao than a evil girl with gesugao.

Anime: Tenjou Tenge 天上天下 (Episode 3)

Textbook definition of scum. Face and everything.

It just happens nobody cares about the dudes, as usual: people only pay attention when girls do it. So much that it's become practically a kind of fetish and consequently a type of fanservice by now.

俺は悪い顔した娘が好きだからよ
いつも笑顔で楽しくやってる艦娘たちも
ちょろっと狂わせてゲス顔悪顔にしちまう男なんだ。
よろしくな pic.twitter.com/YboJXQWJY9
— 海老ブルー💪コミ１-M48a (@ebiblue) November 11, 2018

They don't need to be laughing like a maniac either. Some gesugao are just grinning like an evil potato-chip-eating bastard.

Manga: Death Note (Chapter 53, 悲鳴)

keikaku doori 計画通り
All according to the keikaku.
- Note: keikaku 計画 means "plan."

Not Evil Gesugao

Furthermore, sometimes a character does a gesugao and they aren't evil or anything. It can happen as a joke, in comedy anime, when the character gains some petty advantage over someone else, like winning a bet, or discovering some blackmail material, and then they pretentiously grin in gesugao as if they're now the king of the world.

Anime: Kono Subarashii Sekai ni Shukufuku wo! この素晴らしい世界に祝福を！ (Episode 11, OVA)

Here we have Megumin, acting smug for winning a match of rock-paper-scissors.

There are also those characters that aren't villain evil, but are definitely demons.

Anime: Gabriel DropOut, ガヴリールドロップアウト (Episode 1)

Raphiel rejoices in humiliating others.

Note: in the often posted meme template know your gaos, gesugao is inaccurately labelled "warped evilness."

Not Smiling Gesugao

Since gesugao just means literally "scum face," and not "grinning face" or anything like that, the point of the term isn't that the character is grinning, but that their face lets it show that they're scum. Even though most of the time gesugao shows up in pleasure, sometimes gesugao shows up in displeasure, specially when the character is annoyed, disgusted. or angry with someone.

In Japanese

Linguistically, gesugao ゲス顔 is the word gesu ゲス which means "scum," as in a low-life, with no dignity, waste of oxygen, human-shaped trash, etc. and the word kao 顔 which means "face," the body part, and thus can also mean "expression."^{(dic.pixiv.net:ゲス顔)}

For why kao turns to gao as suffix, see rendaku 連濁.