Speaking as a major anime fan, I've come across a fair share of anti-villains in my reading and viewing experiences. Doesn't ring a bell? Don't worry, let me shed some light on it. An anti-villain could be seen as the mirror image of an anti-hero. While an anti-hero is a protagonist who lacks some of the conventional traits of a hero, an anti-villain is a villain who has some characteristics normally attributed to a hero.
Often, an anti-villain's personal aims are more nuanced than simple world domination or causing chaos for its own sake. This sort of character may have a noble goal or some agreeable qualities, but they engage in questionable actions to accomplish said goal. This purposeful blurring of the moral line is what keeps us glued to the screens or pages because it's always intriguing to relate to a character who, on one hand, does wrong things yet, surprisingly, stands for some rightful causes.
For example, in 'Death Note', Light Yagami serves as a perfect anti-villain. In his eyes, his intentions to rid the world of criminals are virtuous. Yet his methodology, using a supernatural notebook to kill, forces us to question if this is correct.
Similarly, in 'Game of Thrones', we see Jamie Lannister's transformation from seemingly unscrupulous villain to a somewhat redeemable character with a tangible moral compass. It's this complexity and depth that make anti-villains so compelling and often unforgettable.