Biography
Some people can be filled with the desire for Revenge so greatly that they will pursue it at any cost. Their pursuit of it can be unreasonably dangerous to themselves and/or their loved ones (which in extreme cases can make it a Suicide Mission), or it can lead to unreasonable and irrevocable consequence to their mission/objective.
This is mainly a villain trope, not the least of which because the revenge tends to be Disproportionate Retribution caused by the most minuscule of slights, and sometimes targets innocent third parties. If the level of vengeance is taken to a downright ridiculous level, one may end up asking Why Don't You Just Shoot Him? rather than waste time and resources towards humiliating or torturing the person before killing them or making sure that they die horribly in some slow, easily escapable death trap.
Yet heroes can fall into this, showing that even they aren't immune to this flaw. When heroes experience this, it may lead to becoming just like the villains they sought revenge against.
Can't Kill You, Still Need You is a concept that this trope will completely ignore, or will even actively fight against to get at the target of their vengeance.
Often invokes Taking You with Me and Being Evil Sucks. If avenging a death, will be regarded Excessive Mourning. If the character snaps out of it, can lead to Was It Really Worth It? and My God, What Have I Done?. If a character calls them out on their revenge quest then it's Revenge Is Not Justice.
A Sister Trope to Blinded by Rage.
Compare with Freudian Excuse Is No Excuse, Honor Before Reason, Roaring Rampage of Revenge, He Who Fights Monsters, Evil Is Petty, Inspector Javert, Pyrrhic Victory, Revenge Is Not Justice, Stupid Evil, Screw the Money, This Is Personal!, or Personal Hate Before Common Goals.
Contrast with Forgiveness or Restrained Revenge. Success as Revenge is essentially the opposite, giving up on revenge entirely because it's not worth it.