There have been many thoughts on this.
Of course, the main answer is "we'll figure it out once we need to", because when given a problem and the freedom to try different solutions, humans actually tend to come up with some pretty good stuff.

Now, my understanding is that you're asking "what do we do AFTER someone has done bad thing X?", so I won't bother with the multitude of ways that people have suggested for preventing bad thing X from happening in the first place.

Something that I see discussed quite often is, essentially, social ostracism. After all, no one wants to do business with a murder or a rapist, right?
And honestly, you probably don't want to do business with someone who does business with them, either, because that might indicate that they're the kind of people who think that sort of thing's ok.

So, obviously, whenever someone feels that someone else has in some way caused them damage or injury, they could take it to an arbitration organization. Think like court, except without the emo priest robes and the armed quasi-soldiers to make sure you go along with everything the emo priest says. This would tend to sort out lots of stuff that would happen in fits of emotion or drunkenness or simply personal error or misjudgement. Cool beans.

But, lets say you've got that total bastard who doesn't care about property, doesn't care if they hurt someone else, etc. Unlikely to sit down with you and an arbitrator to hash things out, yeah? So, what do you do?

Make an entry into the blockchain.
"This person, description and name of person along with any identifying information refused arbitration/refused to abide by arbitration over an accusation of insert bad thing X here. Until such a time as the issue is resolved to the satisfaction of victim and Acme Arbitration Org, he is blacklisted from all services"
And then he doesn't get any arbitration services from that organization. And they probably have an agreement with their clients that he doesn't get services from them, whatever they do for a living. And the other arbitration organizations probably pick it up too, because they don't want murderers and thieves running around in -their- district/region/whatever either. And they most likely have the same agreement with their clients as well.

And now bad guy Z can't buy food, can't get a haircut, buy gas, rent an apartment, buy property, clothes, get a carwash, hook up with a hooker, go to a bar, etc etc etc until he gets the issue sorted out like he should have in the first place.