- Peruvian citizens (or naturalised Peruvians) who live abroad yet get divorced in Peru and have not updated their Peruvian passport and/or DNI. What often happens is that they got married in Peru while they were young and then left. Years later they decide to get divorced.
- Couples in which one person is Peruvian and the Peruvian has not updated their Peruvian passport and/or DNI. In this case what usually happens is that the Peruvian wants to get married in their country so they have a wedding there for the family, but they live abroad. Then they decide to get divorced.
- Get divorced in the country they are living and then register their foreign divorce in Peru (aka exequatur).
- Get divorced in Peru and register their Peruvian divorce in the country they're living in.
If you are the person living abroad and are Peruvian, you will have to change your DNI so it says you're divorced. If you're a woman and have taken the "de", you will have to change your name on your DNI and passport. In order to do this you will need the proper paperwork.
For marriages that took place in Peru
If you got married in Peru, you will need to get the marriage certificate from the municipality. It will have an annotation on it that states you're divorced. This is the document you will need if you want to update your documents. Hopefully your ex will be nice enough to send them to you (mine wasn't, so I still haven't updated my documents after all this time), if not you can either ask a friend or family member to do it or in the worst case scenario get a lawyer to do it.
For marriages that took place abroad
If you got married abroad, you will have to talk to the embassy or consulate that has jurisdiction over your area to see what the requirements are. More likely than not you're going to have to get things translated and apostillised (or authenticated if the country isn't in the Hague Agreement). Hopefully you got married in the country you're living in. If you got married in one country, divorced in Peru, and are now living in a third country, you will probably run into difficulties. Some people have said they just need their marriage certificate and their Peruvian divorce documents. Other people have said they need to register their Peruvian divorce in the country they're living in. (If you're in the USA, you might have trouble registering (or recording) a foreign divorce. I know that my county no longer registers foreign divorces.)
Either way, you are also going to need your DNI and your passport. If they're not valid, it should be ok and you can still update your records. Whenever you decide to renew your documents, the changes will be reflected on them. You will also need to fill out some forms and pay a fee. Make sure you call the embassy or consulate and see if they have any other requirements.
If you are not able to update your documents for whatever reason and you hold citizenship in another country, then don't worry. You can still get married again. You will just have to show your Peruvian divorce agreement. Make sure it's translated and apostillised (or authenticated if the country isn't in the Hague Agreement).
If you are not able to update your documents and you do not have a second citizenship, then you will have problems if you want to re-marry. You will either have to update your documents, stay single, or simply live together.