Unfortunately back in the times of Ancient Greece there wasn't an established court system so the practice of seeking ones own revenege was practiced.  I personally don't agree with it, but then again I am off the school of thought that believe that criminals should be dealt punishment not revenge.  These two things are very different.  Revenge is simply a physical reaction to the emotional pain being felt by the victim(s) that solves nothing and creates only more pain and suffering for others.  Sure revenge may make you feel better but what about the innocent loved ones of the criminal?  Do they deserve to suffer for a crime someone else commited? Within society revenge does not work.  There is no order to it.  Different people view different crimes in different ways and think that people should be punished differently because of their views.  What one person considers a crime might be seen as nothing by another.  Just look at the lynching during the civil rights movements of the 60's.  White power organizations lynched African Americans as revenge for "stealing their jobs and money" when it was actually revenge against the color of their skin.  How is that just and right?  Without he, albeit flawed, organization of the criminal justice system the world would be a chaotic place with everyone killing and hurting others simply in the name of revenge.  The very nature of revenge goes against the fundamentals of right and wrong that are supposed to be instilled in us from a very early age.