The Idea of Justice

I think the idea of justice is a bit confusing for me. Some say it's good, some say it's bad. What I want to know is, who does it benefit? I don't believe justice benefits anyone anymore. Just like everything else, it's become politics. The Death penalty for example. Some states have it, some do not. Whatever happened to an eye for an eye? If someone kills your child, should they not be euthanized instead of put in a mental hospital? People give the argument that killing another person goes against the unalienable right to Life. Well, the person who killed your child certainly went against that, why can't the government do the same?