In 11th century Iceland, they had a remarkable way of dealing with violent crime. Any time someone was murdered, their relatives would take their case to the Thing (which, yes, is what their assembly was called - neat eh?) where council/officials would decide on a remuneration (and no, there was not a Thing 1 and Thing 2).
Remunerations in the fascinating form they took in Iceland started as a way to end blood feuds: the circular logic of, "you killed of my family! I kill of yours!!"; "yeah???!? well you just killed of my family, so I kill back!!!" There is quite a lot of Icelandic literature dealing with these monstrous feuds, which would frequently drag on for generations until one of the last two people who cared would kill the other one; or until one entire family was massacred and the line was ended. This was devastating... to everyone... for all kinds of obvious reasons.
Anyway the remuneration was paid by the murderer to the victim's family, AND THE WHOLE THING WAS DROPPED.
I repeat: compensation ENDED THE FEUD. Maybe they wouldn't like each other, but there was to be no question that the murdering was done. Shame culture (see part I).
North America (the only place I've really ever known) has a peculiar and uneasy mix of guilt and shame cultures. We put people in prison for certain lengths of time, then release them back into the community. But ex-inmates almost invariably face barriers, EVEN AFTER TIME SERVED, to re-integrating.
A criminal does something horrible and disgusting. They are apprehended and made to live in shame for a period of time dictated by law. Then they are released, to be subjected to shame, as I've said, along the lines of people deciding to "excessively be... asshole[s]" (see "guilt vs. shame I"). Their repute is stained, even though they have, as everyone loves to say, "paid their debt to society". I don't know whether this extra shame comes from people who think the inmate should have that tiny eternal flame of guilt (since, like, Only God may Forgive??) and who figure since they committed a crime in the past, they don't (note lack of logic)...? ???
If the system truly worked, this period of shame would be a be-all and end-all, and stop the human feud. For some people, it does. I have known people who have gone to prison and gotten out, and who now lead far better lives. But I remain convinced they are able to do so because "time in tha slammer" isn't normal, appropriate conversation material - this unjust, irrational shame follows them. And I don't think that's right.
By all means, punish criminals, preferably (I emphasize) by getting some kind of contribution out of them. Then, let them live. It will start to heal us all.