Pre Crisis -> Post Crisis -> Post Infinite Crisis?

[Permanus]

Evidently I'm not alone in being completely baffled by all this. Everywhere I go, I keep running into the same questions, asked, I suspect, with a note of despair. I've pretty much given up on trying to understand it all, but this guy's made a tremendous effort if any of you lot wants to have a look: http://forums.comicbookresources.com/showthread.php?t=88800&page=1

[Captain Kal]

I'll see if I can summarize the various Supergirls since the Crisis.

Matrix Supergirl started out as a protomatter pseudolifeform created by the Pocketverse Luthor.  She had Lana Lang's persona imprinted on her.

When Matrix migrated to the mainstream DCU Earth, she took no other identity while living with the Kents.  She did take on Superman's likeness and identity at one point but her addled mind got better.  She also took Draaga's shape on after Panic in the Sky to honour the noble warrior's self-sacrifice, but mysteriously went to using his classic form again later.

A Kara of Argo was shown, IIRC, in the Superman vs Aliens one-shot.  Argo was colonized by people influenced by Kryptonian culture though they weren't Kryptonians themselves.  I don't think that book is in canon, however, so this is a moot point included just for interest sake.

Power Girl is the Earth-2 version of Kara Zor-el and is evidently once again the multiverse counterpart to the mainstream Kara Zor-El Supergirl.  For a time she was considered the granddaughter of Arion of Atlantis and possibly other retcons on her origin.  Johns has explained this as reality trying to fit her in since she really didn't belong in the Post Crisis DCU.

Andromeda/Laurel Gand and her SW6 duplicate were Daxamite descendants of Lar Gand introduced into the LSH continuity to fill the gap formerly filled by the real Supergirl.

Cir-El was another Supergirl thinking herself the daughter of Lois and Clark but was really a Terran woman of the present imprinted with partial powers based on genes in Superman's hair by Brainiac-13.

Matrix Supergirl eventually merged with a real woman, Linda Danvers, to form PAD's 'Earth Angel' Supergirl.  Eventually, both were split again with Matrix leaving Earth and Linda continuing as a singular Supergirl with most of their former powers.  She has been essentially written out of the current DCU books as no one but PAD gives a hang about her.

PAD introduced a supposed 'real Kara Zor-El' from the SA era in his Earth Angel misguided series.  She returned to her supposed Pre Crisis Earth to live out her destiny to die fighting the Anti-Monitor in the Crisis.

The current Supergirl is the supposed Post Crisis incarnation of Kara Zor-El.  See the current Supergirl book and the recent Superman/Batman intro stories on her.

I think that's it.  Somebody fill in the gaps if I've missed something.

I suspect this huge mess is symptomatic of the fact that no one has ever been able to keep a Supergirl book alive in any era.  It remains to be seen if the current attempt will fare any better.

[Permanus]

Finally, a sensible summarization! Thanks, Cap. They should really have left her memory alone, shouldn't they? As you say, a Supergirl title has never really been viable.

[Daughter of Krypton]

Evidently I'm not alone in being completely baffled by all this. Everywhere I go, I keep running into the same questions, asked, I suspect, with a note of despair. I've pretty much given up on trying to understand it all, but this guy's made a tremendous effort if any of you lot wants to have a look: http://forums.comicbookresources.com/showthread.php?t=88800&page=1

That timeline has been updated here:
https://www.supermanthroughtheages.com/phpBB2/viewtopic.php?p=14815#14815

I'm also pretty sure that all this has already been explained and discussed somewhere in these forums.  Try a Search or browse the Supergirl section.