These poor souls used to be referred to as the "walking wounded", staggering through life, and dating sites, with a figurative knife still deeply planted into their hearts by the ones who left them or died.
They want to move on, to be happy again and find love once more, but....they JUST CAN'T GET OVER the ex.  Some are so blatant as to mention the ex in practically every conversation you have with them.  Some are more careful and some are just silent martyrs to their suffering.

So what to do?

Aside from what I've mentioned above, they otherwise have all these checks in the right-hand column and there's that elusive chemistry kicking around, too.  So many possibilities but you can't get rid of that third person in the room who isn't really there (but seems like they're there all the  time).
Here are some options:
1. If there seems to be potential for a real, fulfilling relationship to bloom, consider couples therapy.
2. Or urge the torch-carrier to seek professional counseling on his or her own.
3.  Make a pact, write it out if you have to and agree that now that your mutual histories are known and understood, you vow to stay in the moment and talk about that and the future.  When infractions occur, correct gently.
4. If there are children involved and communication is necessary, then insist on being left out of squabbles and have your newfound love learn to compartmentalize. Granted, it's tough because kids are naturally going to create gray zones. 5.  If your new-found love agrees to any or all of the above, then be patient.  It's going to take some time to break old habits and avoid intrusive, involuntary thoughts that the torch-carrier has been experiencing for a long time.