Whether the person seeking revenge is the villain or the hero depends on the perspective, the level of culpability of the person against whom revenge is sought, and whether the punishment fits the crime. For example, a young girl who is teased and embarrassed - who seeks revenge by socially humiliating the person who teased her - can probably remain the hero of the story. However, if that same young girl takes an ax and dismembers her teaser - we now have a completely different kind of story - one written by Stephen King, perhaps.
Generally, though, in fiction as in life, revenge is a losing proposition. Edmond Dantes starts out as a victim but becomes more an anti-hero than a hero - he gets his revenge but innocent people die along the way. And the exacting of revenge, no matter how justified, can be a blemish on a character.
So if you're a thriller writer and you want to use a revenge plot, be careful. It's a good motivator for a villain - I'm about to do an extensive re-write and edit of a book where the villain is seeking revenge. A villain seeking revenge for the betrayal of a friendship may still be a villain but at least he's understandable. If, however, your protagonist is seeking revenge - and you want him/her/they to remain sympathetic, the revenge has to be proportionate to the crime.
And in real life?
There's another saying: the best revenge is living well. Well maybe. But stand-up works too.. Alternatively, the best revenge may be sticking someone in your thriller novel - and making them the villain.