I would avoid it, for the most part.
I'm for historical honesty with a romantic partner, especially if you expect the relationship to be long term.
Though, full down-and-dirty details aren't absolutely needed.
I dated Jenny for 3 years, we slept together.
Not; Man, Jenny was a FREAK. I used to do her doggy... and MAN, the stuff she could do with her TONGUE! OH MY GOD! I used to eat Jello out of her butt crack. It was CRAZY! Then we did coke this one time!
Short and simple.
I don't want to know anything about my girlfriend's past. I know she had a boyfriend before me but that's all. I don't know if she had any sexual partners in college, I don't know how many guys she's kissed - nothing. And I don't want to know. The thought of it really makes me jealous and angry. I've even asked her not to talk about her past. Plus, she doesn't like hearing about mine despite it being shorter than hers.
If you are worried about STD stuff, just ask the woman to get tested. If she cares, she will do it. Don't be bashful about it - being responsible is nothing to be ashamed about. I've done it and am glad I did it.
Less is more, in this case.
Note, if I get to the point of a life long commitment, I may ask about this stuff if I didn't already find out. But I really don't know since I've never gotten there. It can be nice knowing everything about the person you love but somethings may be better off never knowing. It's a toss up.
You discuss what is relevant to the present. Regarding STIs, that may or may not involve discussing past relationships. You could just get tested, as has been suggested. Or you could discuss just enough about past relationships to satisfy each other you don't need to get tested. I'd say err on the side of relationship confidentiality and testing, so if one partner wants to talk, and the other wants to get tested, you should get tested and not press for a history.
Regarding relationship issues, my relationships before my husband shaped the person he met. They taught be about myself and what I wanted in a spouse. Lots of these things are personality issues that would have been very hard to explain without just stating my experience. For example, I don't think that punctuality or tracking finances are generally moral matters, but they were things I had to have in my life to feel what's commonly called happy. Other people (such as my husband) may learn such things about themselves in other ways, or be able to express them without giving the history, but I couldn't.
Of course, the longer I'm with my husband, the less my past experiences matter, and the less we talk about them.
My wife knows about all of my relationships and I of hers. Its not something we talk of much. Sometimes it comes up but not as a comparison between her and any one of them.
Like the others, if asked, I talk about it with as much as is necessary but not the super details.
If she wants to share, she can, and they usually do, a little or too much.
We never talk about it. Broad details -- I have dated before -- are enough. Who wants to hear that sort of thing? Knowing she's the only one now is all she cares about.
I answer questions as they arise, however I never bring up ex-girlfriends for any reason if I can avoid it. I never ask her questions about her past relationship. I see no good coming from that.